Double a number increased by five is added to triple a number minus the same number.

Let's call the first number "x" and the second number "y".

"Double a number increased by five" can be written as 2x + 5.

"Triple a number minus the same number" can be written as 3y - y = 2y.

To find the expression for the entire statement, we can add the two expressions together:

2x + 5 + 2y.