Since I live in an apartment (which I still consider moving out of), I've had to consider this as well. Here's what I planned on doing.
1) Get a few buckets. I have some 5g buckets, and some smaller ones (2.5g). Since yours is a 5g tank, the smaller buckets would work best.
2) Put some tank water in two of the buckets.
3) Net out the fish and add them to one of the buckets. Put a few floating plants (if you have any) in with the fish for cover.
4) Take out the plants/decorations and put them in the second bucket.
5) Rinse off the filter media in some leftover tank water, then add it to the plant/decoration bucket.
6) Drain the remaining tank water out of the tank so it just covers the substrate.
You should be able to move the tank and buckets without much of a problem to your new location and set it back up there.
A few notes:
- If you were moving farther, I'd recommend buying a battery operated air pump and air stone to pump air into the bucket with fish in it.
- Some have suggested using fish bags rather than a bucket. I think there are pros and cons to both.
bucket pros
- transport alot of the tank water to mix with water at the new location
- bucket with air pump/stone may help fish survive a longer distance
bucket cons
- water sloshing around in vehicle could cause spilling or injure fish
- aggressive fish cooped up in a small bucket could present a problem
bag pros
- no splashing water, reduces chance of injuring fish
- separating fish might be better for transporting, depending on the fish
bag cons
- need to add chemicals if fish will be in the bag long distances
- won't transport as much of the original tank water to add at new location