Technically yes, but I took my heat lamp off of Pheasants and Silkies at around that time because they were living inside an insulated house and it was getting pretty stuffy. It depends on how hot it is in their brooder, but then the heat should be pretty lowered from when it was younger. Try decreasing the heat and seeing how they react. Judging by their reactions you should be able to tell if they're comfortable with it or not.
Wow, I really didn't read your question well. I thought you were asking if you could take the heat lamp off of a 5 week old turkey. Sorry about that! I'm sure your turkey is fine by now. If his brooder is in a barn or somewhere that gets cold at night then maybe consider having it on at night but otherwise I wouldn't worry about it. It gets pretty hot in these summer days you wouldn't want him to over heat.