To solve this system of equations, we can use the method of elimination.

First, let's add the two equations together:

(x + y) + (x - y) = 5 + 2
2x = 7

Now, divide both sides of the equation by 2 to solve for x:

2x/2 = 7/2
x = 7/2

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

x + y = 5
(7/2) + y = 5

Subtract (7/2) from both sides of the equation:

y = 5 - (7/2)
y = 10/2 - 7/2
y = 3/2

Therefore, the solution to the system of equations is x = 7/2 and y = 3/2.