\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =-5\,x \left ( t \right ) -2\,y \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =x \left ( t \right ) -7\,y \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.013002 (sec), leaf count = 59 \[ \left \{\left \{x(t)\to c_1 e^{-6 t} (\sin (t)+\cos (t))-2 c_2 e^{-6 t} \sin (t),y(t)\to c_1 e^{-6 t} \sin (t)+c_2 e^{-6 t} (\cos (t)-\sin (t))\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 46 \[ \left \{ \left \{ x \left ( t \right ) ={{\rm e}^{-6\,t}} \left ( \sin \left ( t \right ) {\it \_C1}+\cos \left ( t \right ) {\it \_C2} \right ) ,y \left ( t \right ) ={\frac {{{\rm e}^{-6\,t}} \left ( \sin \left ( t \right ) {\it \_C1}+\sin \left ( t \right ) {\it \_C2}-\cos \left ( t \right ) {\it \_C1}+\cos \left ( t \right ) {\it \_C2} \right ) }{2}} \right \} \right \} \]