You almost have to use a 10 gallon cooler for 5 gallon batches... yeah, the 5 gallon cooler works on paper (I know, I did the math, and bought the cooler), but that doesn't take account for vigorous stirring, adding water when your strike temp is a little low, adding mash-out water (if you do that), making "extra" wort to account for trub losses, throwing in an extra couple pounds of grain because your efficiency isn't great and you don't wanna buy your own mill just yet, attempting high-gravity beers .... etc.
Not only will you mash a 5-gallon batch just fine in a 10-gallon cooler; at some point during your first handful of batches, you'll go "dang, this thing's awfully full, wonder if I shouldn't have sprung for the 15-gallon?"