\[ a x y(x)-5 m y^{(4)}(x)+x y^{(5)}(x)=0 \] ✓ Mathematica : cpu = 2.07302 (sec), leaf count = 216
\[\left \{\left \{y(x)\to c_5 5^{-5 m-4} a^{\frac {1}{5} (5 m+4)} x^{5 m+4} \, _0F_4\left (;m+\frac {6}{5},m+\frac {7}{5},m+\frac {8}{5},m+\frac {9}{5};-\frac {a x^5}{3125}\right )+\frac {1}{125} a^{3/5} c_4 x^3 \, _0F_4\left (;\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {4}{5}-m;-\frac {a x^5}{3125}\right )+\frac {1}{25} a^{2/5} c_3 x^2 \, _0F_4\left (;\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {3}{5}-m;-\frac {a x^5}{3125}\right )+\frac {1}{5} \sqrt [5]{a} c_2 x \, _0F_4\left (;\frac {3}{5},\frac {4}{5},\frac {6}{5},\frac {2}{5}-m;-\frac {a x^5}{3125}\right )+c_1 \, _0F_4\left (;\frac {2}{5},\frac {3}{5},\frac {4}{5},\frac {1}{5}-m;-\frac {a x^5}{3125}\right )\right \}\right \}\] ✓ Maple : cpu = 0.187 (sec), leaf count = 118
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_0$F$_4$}(\ ;\,{\frac {2}{5}},{\frac {3}{5}},{\frac {4}{5}},{\frac {1}{5}}-m;\,-{\frac {{x}^{5}a}{3125}})}+{\it \_C2}\,x{\mbox {$_0$F$_4$}(\ ;\,{\frac {3}{5}},{\frac {4}{5}},{\frac {6}{5}},{\frac {2}{5}}-m;\,-{\frac {{x}^{5}a}{3125}})}+{\it \_C3}\,{x}^{2}{\mbox {$_0$F$_4$}(\ ;\,{\frac {4}{5}},{\frac {6}{5}},{\frac {7}{5}},{\frac {3}{5}}-m;\,-{\frac {{x}^{5}a}{3125}})}+{\it \_C4}\,{x}^{3}{\mbox {$_0$F$_4$}(\ ;\,{\frac {6}{5}},{\frac {7}{5}},{\frac {8}{5}},{\frac {4}{5}}-m;\,-{\frac {{x}^{5}a}{3125}})}+{\it \_C5}\,{x}^{4+5\,m}{\mbox {$_0$F$_4$}(\ ;\,{\frac {7}{5}}+m,{\frac {6}{5}}+m,{\frac {9}{5}}+m,{\frac {8}{5}}+m;\,-{\frac {{x}^{5}a}{3125}})} \right \} \]