The length of pull on a stock 10/22 might be a little too long for your 5yo daughter. Since you mentioned precision shooting, look up Cricket Precision Youth rifle. Might be a better fit for your little one. I think I saw one at New Frontier not too long ago.
We have a regular Cricket and my 6 and 8yo daughters love it. My 11yo son likes the 10/22 and a regular ar with cmmg conversion kit.
Precision I would start with single shot, make each one count.
Savage Rascal is a small version of a larger rifle, good adjustable trigger, standard manual safety and not added cocking step. Also comes in many colors.