I have two male guppies in a 5 gal tank and one has been bullying his larger tankmate. Will he bully the other guppy to death? Would moving them to a much larger tank solve the problem?

Do you have other fish in there too? Fish of most any type are more likely to bully each other when there are few fish in a small tank situation. Part of it is boredom, part stress, part frustration if there aren't females around. Male guppies usually get along but it's not unusual to get one that is not so nice to the others. Fish bullying can be fatal. A larger tank will certainly help especially if there are other fish, places to hide, and females. If you don't have other fish in the 5 gallon, you could also put in a divider to separate them; I know they sell one for the 5 gallon that I have.

Good luck Chelsea!