S.,
Hi! I totally understand your plight. I've never been to a private preschool like that, but I can share some of my own experience with you. I started kindergarten at 4, didn't made the cutoff and had to test into it. Everyone in my class was 5 and 6. I graduated high school at 16, so as you can see I was at least 2 years younger than my peers. This resulted in a very miserable social experience for me, as you might imagine. I had the opportunity to switch schools in 3rd grade, but my parents didn't get the scholarship they were planning on, so I didn't get that chance. In my opinion, I would have LOVED to switch schools. Even though I still would have been younger, I could have started over.
This situation isn't the same as your daughter's, but the lesson is similar. I am now 21 years old and STILL am bitter that I didn't get the chance to start over. My problems with being teased and feeling out of place began at 5 years old, and I really wish my parents would have done more to help me. Now, it hasn't ruined my life by any means, but it is something that is upsetting to me. If she were my child, I would move her. With only 4 months left in the school year, I might wait until the year is over, but if she is really unhappy and you are seeing differences at home as well, then her schooling is affecting her life and she should be moved. If you don't see differences at home, then have her stay thru the end of the year (there's your chance to teach her a valuable lesson), but definitely move her next year.
Personally, I want to bring my children up in a montessori school. I tested into one at 4 years old, but my parents were very poor and couldn't afford to send me. I went to high school with 2 people from the montessori school and they were much happier that those of us who went to public school. If you have the opportunity to send your kids to a montessori school (even if the 3 year old loves her other school) I would definitely do it. At 3 years old, she can easily make new friends because she won't be leaving long-time classmates or anything.
If your 5 year old is truly unhappy, and it's spilling into her non-school life, switch schools at spring break or over a weekend before then. You can still make it a lesson for her. Sometimes, it's detrimental to stick something out, but it's the trying that counts. She has tried and done everything in her (and your) power to change her situation and stick it out but it's not working. Sometimes it's necessary to make changes. If children aren't taught that it's ok to make changes when all else fails, they will be stuck in miserable situations forever. So this could be a very powerful lesson.