5 speed cassette on 8 speed hub
The first thing to note is "Does the 8 speed hub clear the dropouts ?" 

You may be able to spread the frame if steel. Since you're likely going from a 120mm to 130 mm (which is 2 sizes - 120->126->130), you should be cold setting it. 

The second question would be "Can the brakes reach the rim?"

Unfortunately, to my knowledge, nobody makes a 5 speed cassette. You'll have to get a 7 or 8 speed cassette and tweak the limit screws on the rear derailleur so you shift in the appropriate range (if indexed, and the sprocket spacing matches the indexing [ I don't think it will, since a 5 speed freewheel should have 5.5 mm, while a 7 or 8 speed cassette 5 mm] ). Alternatively, if you have friction shifters (or can deal with friction shifters), set the limit screws, throw on an 8 speed chain and friction shift. 

However, Velo Orange makes a cheap wheelset which can take a freewheel, and plenty of 5 speed freewheels are still around (e.g. IRD). (Note that you can get 126mm, 130 mm).

My recommendation would be to cold set the frame to a 130 mm hub if you can and use your shifters in friction mode after adjusting the limit screws appropriately with a 7 or 8 speed cassette. If you don't want to cold set the frame, then buy a wheel with a freewheel hub of appropriate spacing (likely 120 mm if it came with a 5 speed freewheel - 120 mm hubs are still made, but I don't know who sells complete wheels so it may need to be built to order), buy a nice 5 speed freewheel from IRD and move on with your life. This will allow you to use indexing if you have it. The latter would be your only option if your frame is not steel.