Whenever I go out with a friend or to work (I mainly work from home, so that's rare), My 5 YO DD protests and screams and cries. Often whoever I'm leaving her with will have to hold her so I can get out the door because otherwise she'd keep clinging to me. If I tell her in advance that I need to go out she'll cry off and on until the time comes. When I do leave, she sometimes cheers up right away, other times she's unhappy until I come home. I don't go out very often, maybe once a week for a few hours at a time, twice at most. She's only in school 6 hours a week, and we still co-sleep, so we have A LOT of time together.
I've tried to talk to her about this and she says that she misses me when I'm gone and wants to be with me all the time. She's an otherwise happy girl and has always been able to separate from me easily when she's going off to her own activities. Her preschool teachers say she's very outgoing and plays well with all the kids.
I'm not one to force independence, if she still needs me all the time, I'll do my best to honor that (within reason, given that I have my own needs and other responsibilities). But it just seems like she's so old to be this upset when I leave, and if there's an underlying insecurity or issue I'd rather address it now.