Express \(x ^ { 2 } + 6 x + 5\) in the form \(( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants.
The curve with equation \(y = x ^ { 2 }\) is transformed to the curve with equation \(y = x ^ { 2 } + 6 x + 5\).
Describe fully the transformation(s) involved.