I dont' so much think it's seperation anxiety. She's just used to Mommy and is learning to distinguish who strangers are. lily is the same way. I can lay her down and start to walk away and she tunes up and screams. She does it when her sister puts her down too.
It sounds like she is just used to being with Mommy. My son did this when he was a baby, I'm a stay at home mom so he was used to it being me and him all the time. I put him in his bouncy chair. He hated a swing, so I used his bouncy seat, or put toys in his playpen or let him snack in his highchair, depending where I was in the house. Sometimes that didn't work, but if he could see me, he was generally ok!
I don't have this problem really yet, but you can tell she prefers me to others. This is normal to start at 5 months.