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

Let's start by solving the first equation for one variable.

5x + 3y = 11
3y = -5x + 11
y = (-5/3)x + 11/3

Now, we can substitute this expression for y into the second equation:

8x + 5((-5/3)x + 11/3) = 15
8x - (25/3)x + (55/3) = 15
(24/3)x - (25/3)x = -40/3
(-1/3)x = -40/3
x = (-40/3) / (-1/3)
x = (40/3) * (3/1)
x = 40

Now that we have found 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:

5(40) + 3y = 11
200 + 3y = 11
3y = 11 - 200
3y = -189
y = -189 / 3
y = -63

Therefore, the solution to the system of equations is x = 40 and y = -63.