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?

the first thing would be to talk to her but i am sure you already did that. other than that, if she has a problem with you handling the baby as such, try doing things that are meant for the baby. or, you can tell your wife that you can help change the baby in front of her, or help put her to sleep.