\[ \boxed { {x}^{10}{\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) -ay \left ( x \right ) =0} \]
Mathematica: cpu = 6.345306 (sec), leaf count = 114 \[ \left \{\left \{y(x)\to c_1 x^4 e^{-\frac {\sqrt [5]{a}}{x}}+c_2 x^4 e^{\frac {\sqrt [5]{-1} \sqrt [5]{a}}{x}}+c_3 x^4 e^{-\frac {(-1)^{2/5} \sqrt [5]{a}}{x}}+c_4 x^4 e^{\frac {(-1)^{3/5} \sqrt [5]{a}}{x}}+c_5 x^4 e^{-\frac {(-1)^{4/5} \sqrt [5]{a}}{x}}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 90 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_0$F$_4$}(\ ;\,{\frac {6}{5}},{\frac {7}{5}},{\frac {8}{5}},{\frac {9}{5}};\,-{\frac {a}{3125\,{x}^{5}}})} +{\it \_C2}\,x {\mbox {$_0$F$_4$}(\ ;\,{\frac {4}{5}},{\frac {6}{5}},{\frac {7}{5}},{\frac {8}{5}};\,-{\frac {a}{3125\,{x}^{5}}})} +{\it \_C3}\,{x}^{2} {\mbox {$_0$F$_4$}(\ ;\,{\frac {3}{5}},{\frac {4}{5}},{\frac {6}{5}},{\frac {7}{5}};\,-{\frac {a}{3125\,{x}^{5}}})} +{\it \_C4}\,{x}^{3} {\mbox {$_0$F$_4$}(\ ;\,{\frac {2}{5}},{\frac {3}{5}},{\frac {4}{5}},{\frac {6}{5}};\,-{\frac {a}{3125\,{x}^{5}}})} +{\it \_C5}\,{x}^{4} {\mbox {$_0$F$_4$}(\ ;\,{\frac {1}{5}},{\frac {2}{5}},{\frac {3}{5}},{\frac {4}{5}};\,-{\frac {a}{3125\,{x}^{5}}})} \right \} \]