\[ \boxed { x{\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) - \left ( aA_{{1}}-A_{{0}} \right ) x-A_{{1}}- \left ( \left ( aA_{{2}}-A_{{1}} \right ) x+A_{{2}} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( \left ( aA_{{3}}-A_{{2}} \right ) x+A_{{3}} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( \left ( aA_{{4}}-A_{{3}} \right ) x+A_{{4}} \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( \left ( aA_{{5}}-A_{{4}} \right ) x+A_{{5}} \right ) {\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}y \left ( x \right ) =0} \]
Mathematica: cpu = 84.450724 (sec), leaf count = 148 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817} A(0)-\unicode {f817} a A(1)-A(1)+(\unicode {f817} A(1)-\unicode {f817} a A(2)-A(2)) \unicode {f818}'(\unicode {f817})+(\unicode {f817} A(2)-\unicode {f817} a A(3)-A(3)) \unicode {f818}''(\unicode {f817})+(\unicode {f817} A(3)-\unicode {f817} a A(4)-A(4)) \unicode {f818}^{(3)}(\unicode {f817})+(\unicode {f817} A(4)-\unicode {f817} a A(5)-A(5)) \unicode {f818}^{(4)}(\unicode {f817})+\unicode {f817} \unicode {f818}^{(5)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3,\unicode {f818}^{(3)}(1)=c_4,\unicode {f818}^{(4)}(1)=c_5\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.124 (sec), leaf count = 119 \[ \left \{ y \left ( x \right ) =\int \!{\it DESol} \left ( \left \{ -{ \frac { \left ( axA_{{2}}-xA_{{1}}+A_{{2}} \right ) {\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{{3}}-xA_{{2}}+A_{{3}} \right ) { \frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{{4}}-xA_{{3}}+A_{{4}} \right ) {\frac {{\rm d}^{2}}{ {\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{ {5}}-xA_{{4}}+A_{{5}} \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{ \it \_Y} \left ( x \right ) }{x}}+{\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}{ \it \_Y} \left ( x \right ) -{\frac {axA_{{1}}-xA_{{0}}+A_{{1}}}{x}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \,{\rm d}x+{\it \_C1} \right \} \]