Complete the square on the following quadratic function $y=2 x^{2}+12 x+5$ and determine the vertex and the axis of symmetry.
Find the axis of symmetry: $x=\boxed{-3}$
Step 1 :Factor out the coefficient of the $x^2$ term: $y=2(x^2+6x)+5$
Step 2 :Add and subtract the square of half of the coefficient of the $x$ term inside the parentheses: $y=2(x^2+6x+9-9)+5$
Step 3 :Simplify the expression: $y=2((x+3)^2-9)+5$
Step 4 :Expand and simplify: $y=2(x+3)^2-18+5$
Step 5 :Final vertex form: $y=2(x+3)^2-13$
Step 6 :Find the vertex: $h=-3$, $k=-13$, vertex $\boxed{(-3, -13)}$
Step 7 :Find the axis of symmetry: $x=\boxed{-3}$