Use f(0)=9\displaystyle {f{{\left({0}\right)}}}={9} and f(1)=1\displaystyle {f{{\left({1}\right)}}}=-{1} to compute f(5)\displaystyle {f{{\left({5}\right)}}}  given:

 f(w+2)=5f(w)+8f(w+1)\displaystyle {f{{\left({w}+{2}\right)}}}=-{5}{f{{\left({w}\right)}}}+{8}{f{{\left({w}+{1}\right)}}} 

 f(5)=\displaystyle {f{{\left({5}\right)}}}=