My 5-year-old girl is not fond of my brother's 13-year-old daughter. She was born in front of me and I was with her during her growing up years, and my best niece. How do I help bond them?

The age difference is actually quite big. They belong to different age groups. Any particular reason that she is not found of her cousin? Don't try too hard to help them bond. You are attached to your niece doesn't mean that your daughter should be equally attached to her. Might be your fondness for her makes her jealous! Keep a track of your own behavior. Also talk to your daughter and tell her that Didi loves her and is elder sister with whom she can share things. Take them both for an outing.