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#### ANSWER : 4 numbers, they are 32,46,96,69.

Let 2 digits of number are x,y.

The given condition is

x+y=5(x-y);

x+y=5x-5y;

4x=6y;

x/y=3/2:

from the above condition we can get following pairs.

(x=3,y=2);

(x=6,y=4);

(x=9,y=6);

combinations of above pairs are 32,23,64,46,96,69.

in those numbers 64 is perfect square, 23 is prime number.

so the 2-digit numbers are 32,46,96,69.