\(\displaystyle{g{{\left({x}\right)}}}={2}-{\left({x}+{5}\right)}^{{2}}\)

\(\displaystyle{f}{1}{\left({x}\right)}={f{{\left({x}+{5}\right)}}}={\left({x}+{5}\right)}^{{2}}\)

\(\displaystyle{f}{2}{\left({x}\right)}={f}{1}{\left({x}\right)}=-{\left({x}+{5}\right)}^{{2}}\)

\(\displaystyle{g{{\left({x}\right)}}}={f}{2}{\left({x}\right)}+{2}=-{\left({\left({x}+{5}\right)}^{{2}}\right)}+{2}\)