To solve the equation 3xy - 5 = x^2 + 2y, we can rearrange the terms to get all the variables on one side of the equation:

x^2 - 3xy + 2y - 5 = 0

Next, we can factor the equation:

(x - 5)(x + 1) - 3y(x - 5) = 0

Now, we can simplify the equation:

(x - 5)(x + 1 - 3y) = 0

This equation will be true if either (x - 5) = 0 or (x + 1 - 3y) = 0.

Case 1: x - 5 = 0
Solving for x, we get x = 5.

Case 2: x + 1 - 3y = 0
Solving for x, we get x = 3y - 1.

Therefore, the solutions to the equation 3xy - 5 = x^2 + 2y are x = 5 and x = 3y - 1.