My wife just does not let me take care of the baby. My baby is 5 mths old now. It drives me nuts and I tried reasoning with her but she is becoming very hard to deal with. What do I do so that she trusts me more?

Let's pin point the reason. don't take care of baby but care for her stuff like prepare baby bed @ night, get something for baby or wife twice or thrice a week like nice wear or toy or hand gloves or anything that u think fits ur baby or your wife will love to see. make some funny gesture to make baby play with u.. let your wife notice that and figure out what she reacts to best.