\[ \boxed { 5\, \left ( ax+b \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +8\,a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +c\sqrt [5]{ax+b}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.047006 (sec), leaf count = 108 \[ \left \{\left \{y(x)\to \frac {3 a c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}+\frac {6 a c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\sinh \left ( {\frac {1}{3\,a} \left ( ax+b \right ) ^{{\frac {3}{5}}}\sqrt {-5\,c}} \right ) \left ( a x+b \right ) ^{-{\frac {3}{5}}}}+{{\it \_C2}\cosh \left ( {\frac {1}{3\, a} \left ( ax+b \right ) ^{{\frac {3}{5}}}\sqrt {-5\,c}} \right ) \left ( ax+b \right ) ^{-{\frac {3}{5}}}} \right \} \]