\[ \boxed { {\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) +2\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -ax-b\sin \left ( x \right ) -c\cos \left ( x \right ) =0} \]
Mathematica: cpu = 0.621079 (sec), leaf count = 104 \[ \left \{\left \{y(x)\to \frac {a x^2}{2}+\frac {1}{8} b \left (x^2-2\right ) \cos (x)-\frac {3}{8} b x \sin (x)-\frac {5}{16} b \cos (x)-\frac {1}{8} c \left (x^2-2\right ) \sin (x)+c_2 x \sin (x)+\frac {9}{16} c \sin (x)+c_1 \sin (x)+c_4 \sin (x)-\frac {5}{8} c x \cos (x)-c_4 x \cos (x)+c_2 \cos (x)-c_3 \cos (x)+c_5\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 78 \[ \left \{ y \left ( x \right ) =-{\frac {\sin \left ( x \right ) bx}{2}}-{ \frac {3\,b\cos \left ( x \right ) }{4}}-{\frac {\cos \left ( x \right ) c x}{2}}-{\frac {\sin \left ( x \right ) c{x}^{2}}{8}}+{\frac {21\,\sin \left ( x \right ) c}{32}}+{\frac {\cos \left ( x \right ) b{x}^{2}}{8}}+ {\frac {a{x}^{2}}{2}}+{\it \_C1}\,\sin \left ( x \right ) -{\it \_C2}\, \cos \left ( x \right ) +\sin \left ( x \right ) {\it \_C3}\,x+\cos \left ( x \right ) {\it \_C3}-\cos \left ( x \right ) {\it \_C4}\,x+{\it \_C4}\,\sin \left ( x \right ) +{\it \_C5} \right \} \]