A mash-tun that is the same as your batch size can make a beer up to about 1.050 gravity. You can squeeze a couple extra points out by filling it to the brim, or with a really thick mash....but, I've done that a few times and it kinda sucks all the fun out of a brew.
A mash tun that is twice your batch size allows you to make pretty much anything below 1.100. It might still be a struggle to make a 1.120 all-grain, barley-wine. In that case though extract or simple sugar is almost always part of the grain bill anyway.
I used a 5 gallon round cooler for many years. It worked fine for all those 1.050-1.055 "standard" beers. Both of the round coolers make for a very deep grain bed, when full. This CAN be an issue for causing a stuck sparge. I never had any actually get STUCK, but I did have a few that drained VERY slow. I would be concerned that the 10 gallon would be worse if it were full. I know a lot of people use them successfully though.
I have a 12 gallon Ice Cube, now. I simply moved by old 5 gallon round false-bottom over to the cube. NOTE: I batch sparge. The small false bottom would not be ideal if I fly-sparged. I wouldn't get good flow near the cooler walls, especially in the corners. But, since I batch sparge..its a non-issue. I like the shorter mash-bed afforded by the greater footprint of the Ice Cube. Plus, the Ice Cube coolers are a lot cheaper for the volume you get compared to the round coolers.
With the 12 gallon cube I can easily stir the mash without worrying about splashing over the sides. I can drain without worrying about stuck sparge. I can basically make any beer I want, 5 gallons up to 1.110ish, 10 gallons up to 1.070ish, 15 gallons 1.045ish.