To complete the square, we see that the second number in the square must be -1. So, "taking" a 1 from the 4, we get:
Now, we can see that if we take the y to the other side, we get the equation in vertex form. So, this will become:
Divide both sides by -1:
Since this is in vertex form, we see that the vertex is at (1, 5)
We can graph this on desmos: https://www.desmos.com/calculator
And we see that our answer is correct.
So, the vertex is at (1, 5)