\[ a x y(x)-5 m y^{(4)}(x)+x y^{(5)}(x)=0 \] ✓ Mathematica : cpu = 2.06916 (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 = 0.271 (sec), leaf count = 118
\[y \relax (x ) = c_{1} \hypergeom \left (\left [\right ], \left [\frac {2}{5}, \frac {3}{5}, \frac {4}{5}, \frac {1}{5}-m \right ], -\frac {x^{5} a}{3125}\right )+c_{2} x \hypergeom \left (\left [\right ], \left [\frac {3}{5}, \frac {4}{5}, \frac {6}{5}, \frac {2}{5}-m \right ], -\frac {x^{5} a}{3125}\right )+c_{3} x^{2} \hypergeom \left (\left [\right ], \left [\frac {4}{5}, \frac {6}{5}, \frac {7}{5}, \frac {3}{5}-m \right ], -\frac {x^{5} a}{3125}\right )+c_{4} x^{3} \hypergeom \left (\left [\right ], \left [\frac {6}{5}, \frac {7}{5}, \frac {8}{5}, \frac {4}{5}-m \right ], -\frac {x^{5} a}{3125}\right )+c_{5} x^{5 m +4} \hypergeom \left (\left [\right ], \left [\frac {9}{5}+m , \frac {8}{5}+m , \frac {7}{5}+m , \frac {6}{5}+m \right ], -\frac {x^{5} a}{3125}\right )\]