let 'x' and 'y' be the numbers and x>y

one whole number is 5 less than another and x>y thus

y = x - 5

the largest number and the square of the smallest have a sum of 61

x + y^2 = 61

by solving the system of equations

y = x - 5

x + y^2 = 61

we find two solutions

First solution:

x = 12

y = 7

Second solution:

x = -3

y = -8

the numbers are 12 and 7.

the numbers are -3 and -8.