Starting Solids

My 5 month old baby has been showing all the signs of being ready to eat table food for a while now but I was waiting for the 6 month mark. The past couple weeks she has been so interested in my food to the point of trying to snatch it from my hand and opening her mouth when I take a bite. I gave in and fed her some mashed fruit thinned with breast milk today. To my surprise she ate almost 2 tbsp even after a full feed. The next feeding time she was very fussy and I kept giving her more milk but she wasn't satisfied and kept crying until she fell asleep. I know she wanted some more food but I want to ease her into solids instead of going full force. Has anyone dealt with this before? Should I give her what she wants as long as she is still taking her milk beforehand?