\[ \boxed { {\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) -axy \left ( x \right ) -b=0} \]
Mathematica: cpu = 0.152519 (sec), leaf count = 61 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-b-\unicode {f817} a \unicode {f818}(\unicode {f817})+\unicode {f818}^{(5)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4,\unicode {f818}^{(4)}(0)=c_5\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]