If you plan on batch sparging, it should work fine for 5 gallon batches.
If you plan on fly sparging, you will have two obstacles to overcome with that setup. The first issue is the fact that a single hose braid like that is going to cause channelling issues when fly sparging. Generally speaking, you'll be leaving large pockets of grain that go "unrinsed" as the sparge water bypasses them and runs straight to the hose braid, leaving you with really low efficiency. You could swap the hose braid out and use a manifold, which would help, but you still have another obstacle...
The second issue is that for a 5 gallon batch of low to medium gravity you aren't going to have enough grain in there to create a deep grain bed. It will be shallow and wide, which also contributes to channeling issues, even if you use a manifold. It's too easy for water to form short channels, drilling from the top of the grain bed straight to the exit points, and not contact much of the grain along the way. It's better to have a grain bed that's deeper and not as spread out, so that the sparge water has to travel through more grain on its way out, increasing the likelihood that you will rinse out any sweet wort and it will end up in your kettle rather than stuck in the spent grains.
It's kinda hard to change the shape of a cooler, so just think about whether you want to fly sparge before you buy.
Palmer talks alot about lautering methods, MLT design etc. Here's a page with some visuals that might help make more sense of my ramblings:
How to Brew - Appendix D2
So if you really want that cooler, just batch sparge and forget about the above. You are just draining off the mash liquid, refilling, stirring it all up, then draining again (and repeating if necessary) so most of the points I've raised become moot.
And of course, there are some people who claim great efficiency even when fly sparging in rectangular picnic coolers and using a short hose braid, even though it's not an ideal setup, so take all my advice with a pint of homebrew.