I would say that they may be alright if you took the lamp but 5 weeks is a bit young and it may be a good idea to let them have the heat for another week or even two. There are so many variables regarding local climate, brooder types and chicken breeds that it's hard to say to be perfectly honest. Usually, once they're fully feathered out, they are pretty tough. Someone posted earlier in this thread that chicks can handle 70 degrees by 6 weeks of age. I think that sounds about right.
I've raised chicks several times and I always tend to be a bit over protective but I've yet to lose a chick while raising them.