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

First, let's solve the second equation for x:
x - y = 14
x = y + 14

Now we can substitute x = y + 14 into the first equation:
2(y + 14) - 5y = 16
2y + 28 - 5y = 16
-3y + 28 = 16
-3y = -12
y = 4

Now that we have found the value of y, we can substitute it back into x = y + 14 to find x:
x = 4 + 14
x = 18

Therefore, the solution to the system of equations is:
x = 18
y = 4