If the difference between two numbers is 5 and the difference between the in cubes is 1850, then the difference between their squares is:

$5\sqrt{485}$

Let the numbers be x and y

According to the question,

x - y = 5

x³ - y³ = 1850

We know that,

(a - b)³ = a³ - b³ - 3ab(a-b)

(5)³ = 1850 - 3ab(5)

125 = 1850 - 15ab

15ab = 1725

ab = 115

We also know that,

If x - y  = n

then, x + y  = \(\sqrt {n^2 + 4xy}\)

then, x + y  = \(\sqrt {5^2 + 4(115)}\)

x + y  = \(\sqrt {5^2 + 4(115)}\)

x + y  = \(\sqrt {485}\)

The difference between their squares is = x² - y² = (x + y)(x - Y)

= x² - y² = $5\sqrt{485}$