selecive mutism, anxiety in daughter

What you're describing here IS the autistic difference. We tend to make friends with much older or younger individuals. When young, adults who appear dependable and stable are much more enjoyable to speak with. Due to not maturing with peers, we might simply observe until we can work out how to engage. 

One's self esteem is developed over a long period of time. At her age, she's yet to learn to recognise her rich, wonderful and wild self, understand her human flaws, laugh at her control issues (we all have them), see the parts still in development, approve and respect her own nature and self-discipline with reason, her own growth so to better use agency to assert boundaries, understand what is human in another and make grounded choices which, in turn, reinforce a sense of being and contentment with the self. 

At 5 we are still making sense of the world, but even sometimes still at 50 :) 

If a child appears controlling on the surface, it means they are experience something which feels dangerous, could sweep them away, beyond their control and trying desperately to navigate. Or they might have a pre-envisioned plan which they are looking to resolve or fulfil and it's important to make room for this, even envision it with them, so you can feel a little more in control if need be. With young children, we need to always provide more time than we think for transitions, as they cannot handle smash-cut interruptions. Very few things are of consequence. 

Children can never actually be controlling, rather looking to us for respect, protection and aid. Rather, old chaps in charge of banks are controlling. I rarely said no to my son on my grandmothers advice. So when I did, he took it seriously. 

Her asserting a need for one to one is actually brilliant. It is part of her ability to focus and you'll want to reinforce and always affirm this. And then help her learn to steer / temper / direct it as she grows. For autistics, if we are vigilant about doing everything one-thing-at-a-time, we will find a better flow and avert harm. We function better like this. What you'll need to do is reinforce her worth while managing her expectations. So, if she needs to speak to you while you're on the phone, ask the individual you're speaking with for a minute. Focus on the child and tell them "I want to listen, you're important. And first I need to finish this. Give me (an exact amount of minutes) and then I can focus on you." Then make sure to follow through to the exact minute. This helps them learn to trust you. It teaches them how they will eventually act in a similar situation when older. 

The term "Aut" in Autistic means Auto, autonomous. It was conceived by Grunya Sukhareva. 

My self-esteem has been grown in part as I take control - or rather - responsibility - for my own life, for my own research in understanding the physical and social world. In short, the library has aided my self-esteem. Good mentors and teachers have helped grown my self esteem, while peers around are busy trying to 'fit in' with a Neurotypical social/tribal and often Freudian "neurotic" mode of being, it is wisdom and sound guidance, building ethics and aesthetics that has crafted mine, along with learning to integrate my actions, words and deeper truths / intents of the self. And then there is the never ending immersion in creative and spiritual endeavours which grow contentment and ease of self. I have so much to learn and my being isn't fulfilled in the ways my non-autistic friends need. 

Perhaps your daughter is perfect for you to invite over your single friends. The ones without kids. It sounds to me like she has a good sense of self. I don't know anyone who likes rejection, so her response is appropriate. The intensity of the response is autistic - we sense-perceive everything with a greater impact, internal and external. This is one defining feature and can work for us along side knowledge. The quicker our response, the better. As she grows she may begin to realise she doesn't actually want to be friends with just anyone. And that's a good place to be. 

What you're describing here IS the autistic difference. We tend to make friends with much older or younger individuals. When young, adults who appear dependable and stable are much more enjoyable to speak with. Due to not maturing with peers, we might simply observe until we can work out how to engage. 

One's self esteem is developed over a long period of time. At her age, she's yet to learn to recognise her rich, wonderful and wild self, understand her human flaws, laugh at her control issues (we all have them), see the parts still in development, approve and respect her own nature and self-discipline with reason, her own growth so to better use agency to assert boundaries, understand what is human in another and make grounded choices which, in turn, reinforce a sense of being and contentment with the self. 

At 5 we are still making sense of the world, but even sometimes still at 50 :) 

If a child appears controlling on the surface, it means they are experience something which feels dangerous, could sweep them away, beyond their control and trying desperately to navigate. Or they might have a pre-envisioned plan which they are looking to resolve or fulfil and it's important to make room for this, even envision it with them, so you can feel a little more in control if need be. With young children, we need to always provide more time than we think for transitions, as they cannot handle smash-cut interruptions. Very few things are of consequence. 

Children can never actually be controlling, rather looking to us for respect, protection and aid. Rather, old chaps in charge of banks are controlling. I rarely said no to my son on my grandmothers advice. So when I did, he took it seriously. 

Her asserting a need for one to one is actually brilliant. It is part of her ability to focus and you'll want to reinforce and always affirm this. And then help her learn to steer / temper / direct it as she grows. For autistics, if we are vigilant about doing everything one-thing-at-a-time, we will find a better flow and avert harm. We function better like this. What you'll need to do is reinforce her worth while managing her expectations. So, if she needs to speak to you while you're on the phone, ask the individual you're speaking with for a minute. Focus on the child and tell them "I want to listen, you're important. And first I need to finish this. Give me (an exact amount of minutes) and then I can focus on you." Then make sure to follow through to the exact minute. This helps them learn to trust you. It teaches them how they will eventually act in a similar situation when older. 

The term "Aut" in Autistic means Auto, autonomous. It was conceived by Grunya Sukhareva. 

My self-esteem has been grown in part as I take control - or rather - responsibility - for my own life, for my own research in understanding the physical and social world. In short, the library has aided my self-esteem. Good mentors and teachers have helped grown my self esteem, while peers around are busy trying to 'fit in' with a Neurotypical social/tribal and often Freudian "neurotic" mode of being, it is wisdom and sound guidance, building ethics and aesthetics that has crafted mine, along with learning to integrate my actions, words and deeper truths / intents of the self. And then there is the never ending immersion in creative and spiritual endeavours which grow contentment and ease of self. I have so much to learn and my being isn't fulfilled in the ways my non-autistic friends need. 

Perhaps your daughter is perfect for you to invite over your single friends. The ones without kids. It sounds to me like she has a good sense of self. I don't know anyone who likes rejection, so her response is appropriate. The intensity of the response is autistic - we sense-perceive everything with a greater impact, internal and external. This is one defining feature and can work for us along side knowledge. The quicker our response, the better. As she grows she may begin to realise she doesn't actually want to be friends with just anyone. And that's a good place to be.