There is a two-digit number which is equal to five times the sum of its digits. Also, if you add the sum of its digits to the number, the order of the digits is reversed. What number is it?

Let the digits be xy.

The number will be 10x + y.

The sum of the digits is then x + y,

and you are told that:

5(x + y) = (10x + y)... (1)

Finally, you are told that if:

(x + y) + (10x + y)

then it is equal to 10y + x, or

x + y + 10x + y = 10y + x... (2)

You have two equations and two unknowns. I think you can work it out now :)