Chad uses 2 crackers for each "sandwich" and has 5 sandwiches a night so he eats 2*5 = <<2*5=10>>10 crackers a night
The box has 4 sleeves of crackers and each sleeve has 28 crackers for a total of 4*28 = <<4*28=112>>112 crackers
1 box has 112 crackers so 5 boxes will have 112*5 = <<112*5=560>>560 crackers
He eats 10 crackers a night and 5 boxes have 560 crackers so they will last him 560//10 = <<560//10=56>>56 nights
#### 56