How many acres? 5 deer on a small place is a LOT. Keep that up for a couple years and you will truly have no deer.
Though, often that is the case, some places are able to withstand that kind of harvest. My Dad could shot 15+ deer a year on his little 5 acre hill country lot and there'd only be more deer next year than there are now. Some places just have insanely high deer densities. It is no thing to see 25 different deer within the first 10 minutes of the feeder going off.
Walk the night, travel light, cross the Rio Grande
Someone strums a mandolin, soft gulf breezes blow
My new life is waiting in old Mexico
-Robert Earl Keen