Title says it all: Could I ferment a five gallon batch on top of the yeast cake from a finished one gallon batch?
Sure. This amounts to a large starter, so you may be slightly overpitching, but I've used the yeast cake from a 5 gallon batch to ferment another 5 gallon batch and had no issues. Depending on the style you are brewing, this could change the flavor somewhat, so to get an optimal pitching rate you could use a yeast calculator and discard part of your yeast cake. However this probably won't make much of a difference, other factors such as temperature will play a much larger role.
Also, if you aren't washing the yeast, you generally you want to ferment a similar style or darker beer the second time around to avoid clashing flavors.