To solve this equation, we can first distribute the -5 to both terms inside the parentheses:

-5 x - 5 3 + 3 = -17
-5x - 15 + 3 = -17

Next, combine like terms:

-5x - 12 = -17

Now, we can isolate the variable x by adding 12 to both sides of the equation:

-5x = -17 + 12
-5x = -5

Finally, we divide by -5 to solve for x:

x = -5 / -5
x = 1

Therefore, the solution to the equation -5 * (x + 3) + 3 = -17 is x = 1.