To solve the equation, first distribute the 3 on the left side of the equation:

3*(x+2) - 5 = 13
3x + 6 - 5 = 13

Combine like terms:

3x + 1 = 13

Now, isolate the variable by subtracting 1 from both sides:

3x = 12

Divide by 3 on both sides to solve for x:

x = 4

Therefore, the solution to the equation 3*(x+2)-5=13 is x = 4.