upper and lower bound

565 kg to the nearest 5 kg  means that the total weight of the people on

board, W,   could be represented as

562.5 < W < 567.5

But Fred's weight, F, could be represented as

87.5 < F < 88.5

Let's assume the lower bound for Fred....this makes the elevator as heavy as possible 

So....when he gets out of the elevator......the greatest possible total weight will now be  less  than

567.5 - 87.5  =    480 kg

So...it is safe to ride