Find the largest number of 5-digits which is exactly divisible by 57.

The largest 5-digit number is 99,999.

To find the largest 5-digit number exactly divisible by 57, divide 99,999 by 57 and subtract the remainder from 99,999.

$\begin{array}{l} \phantom{x^2 }{\quad1754} \ 57\overline{\smash{\big)}99999} \ \phantom{x)}\phantom{}\underline{-57} \ \phantom{{x^2 }+} 429 \ \phantom{{x} )))}\underline{-399} \ \phantom{{x^2 } + 2x } 309 \ \phantom{{x} +1)}\underline{-285} \ \phantom{{x^2 + 3x +)}} 249 \ \phantom{{x} + 1x +}\underline{-228} \ \phantom{{x^2 + 3x + 1)}} 21\ \end{array}$

The remainder when 99,999 is divided by 57 is 21.

Therefore, 99,999 − 21 = 99,978.

Hence, the largest 5-digit number which is exactly divisible by 57 = 99,978.