Is it a must to put my baby on a bottle, can she drink a sippy cup. 5 months old. breastfed, and she doesn't want the bottle or dummy? she will still drink breast mornings and evenings?

You need to do what works for you. If you are willing to sit there & calmly monitor an infant that age sipping the cup contents making sure it des not take too much at a time it would be fine. Five months is a bit early for many to grasp the idea but some will. Bottles are just a convenience that mimics breast feeding & is easier for most infants to regulate flow.