Let the two digit number be "xy" that is to say 10*x + y

So

5(x + y) + (x*10 + y) = (10*y + x)

5x + 5y + 10x + y = 10y + x

14x = 4y

7x = 2y

Now, each of x and y must be an integer between 0 and 9 inclusive. Thus 2y is an integer no greater than 18. Thus x may only be 1 or 2. (If x = 0 then y = 0, but "xy" is supposed to be a two digit number and "00" is technically not a two digit number.)

So if x = 1:

7 = 2y ==> y is not an integer.

If x = 2:

14 = 2y ==> y = 7

So your number is 27.

5*(2 + 7) + 27 = 5*9 + 27 = 45 + 27 = 72 (Check!)

-Dan