\[ a y^{(4)}(x)-f(x)+y^{(5)}(x)=0 \] ✓ Mathematica : cpu = 451.125 (sec), leaf count = 117
\[\left \{\left \{y(x)\to (\text {Integrate$\grave { }\$\$$a$\$$2441918}-1) (\text {Integrate$\grave { }\$\$$a$\$$2570737}-1) (\text {Integrate$\grave { }\$\$$a$\$$2602782}-1) (x-1) e^{-a \text {Integrate$\grave { }\$\$$a$\$$2608758}} \left (\text {Integrate}\left [e^{a K[1]} f(K[1]),\{K[1],1,\text {Integrate$\grave { }\$\$$a$\$$2608758}\},\text {Assumptions}\to (\Im (\text {Integrate$\grave { }\$\$$a$\$$2441918})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$2570737}<\text {Integrate$\grave { }\$\$$a$\$$2441918}\lor \text {Integrate$\grave { }\$\$$a$\$$2441918}<\text {Integrate$\grave { }\$\$$a$\$$2570737}<1)\land (\Im (\text {Integrate$\grave { }\$\$$a$\$$2570737})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$2602782}<\text {Integrate$\grave { }\$\$$a$\$$2570737}\lor \text {Integrate$\grave { }\$\$$a$\$$2570737}<\text {Integrate$\grave { }\$\$$a$\$$2602782}<1)\land (\Im (\text {Integrate$\grave { }\$\$$a$\$$2602782})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$2608758}<\text {Integrate$\grave { }\$\$$a$\$$2602782}\lor \text {Integrate$\grave { }\$\$$a$\$$2602782}<\text {Integrate$\grave { }\$\$$a$\$$2608758}<1)\land (\Im (x)\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$2441918}<x\lor x<\text {Integrate$\grave { }\$\$$a$\$$2441918}<1)\right ]+c_1\right )+c_5 x^3+c_4 x^2+c_3 x+c_2\right \}\right \}\]
✓ Maple : cpu = 0.033 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{-ax}}{\it \_C1}}{{a}^{4}}}+{\frac {f{x}^{4}}{24\,a}}+{\frac {{\it \_C2}\,{x}^{3}}{6}}+{\frac {{\it \_C3}\,{x}^{2}}{2}}+{\it \_C4}\,x+{\it \_C5} \right \} \]