\[ a y^{(4)}(x)-f(x)+y^{(5)}(x)=0 \] ✗ Mathematica : cpu = 300.033 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.03 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{-ax}}{\it \_C1}}{{a}^{4}}}+{\frac {f{x}^{4}}{24\,a}}+{\frac {{\it \_C2}\,{x}^{3}}{6}}+{\frac {{\it \_C3}\,{x}^{2}}{2}}+{\it \_C4}\,x+{\it \_C5} \right \} \]