Question 77301
Factor out -1

{{{-(x^2 + 6x + 5)}}}

Complete the square of the quadratic in the parenthesis

*[invoke completing_the_square 1, 6, 5]

So the quadratic {{{-x^2-6x-5}}} becomes

{{{-((x+3)^2-4))}}}


{{{-(x+3)^2+4)}}}
Here are the graphs of {{{-x^2-6x-5}}} and {{{-(x+3)^2 +4}}} to verify

{{{ graph( 300, 200, -6, 5, -10, 10, -x^2-6x-5) }}} graph of {{{-x^2-6x-5}}}


{{{ graph( 300, 200, -6, 5, -10, 10, -(x+3)^2 +4) }}} graph of {{{-(x+3)^2 +4}}}

Vertex: (-3,4)

Note: you were on the right track but this step
{{{-(x+3)^2 -9-5}}}
should be
{{{-(x+3)^2 +9-5=-(x+3)^2+4}}}