Hi hun
Tbh mess with the sippy is to be expected
It's great that you're trying her with one early, and 5.5mo is a great age to just let her play with it. Is she on solids yet? Really at 5.5mo they don't "need" water per se (tap water from 6mo is ok btw)
I wouldn't worry about her not taking much water from it, just letting her play and experiment with it is great
Maybe only put a tiny bit of water in? I used the Tommy Tippee suitable from 4mo with both my girls.
x