Let us assume the two numbers be x and y, where x > y

So, according to question we have:

x – y = 5 …(i)

x² – y² = 65 …(ii)

Now, by dividing (ii) by (i) we get:

x + y = 13 …(iii)

Now, adding (i) and (ii) we get:

2x = 18

Putting the value of x in (iii), we get:

9 + y = 13

y = 13 – 9

y = 4

∴ The two numbers are 9 and 4