To "estimate," choose values that are close to those given in the problem, but may be comfortably used in calculations.
There are 5280 feet in a mile. So, that's exactly 1056 lengths of 5 feet each. To estimate, 5250 is 5*1050 lengths (and that's easy and pretty close).
In each 5 ft by 5 ft square, 8 people fit comfortably. So, estimating, 8*1050 is 8400 (remember, quick and easy are important in estimating).
To check (or verify), 8(5280/5) = 8448 exactly. Our estimate is close enough.