a11=1;
a15=-2;
a21=-3;
a25=5;
w0=0.5;
alpha0=0.2;
h=0.05;
tt=5;
qq={wz'[t]==a11 *alpha[t]+a15* wz[t], alpha'[t]==a21 alpha[t]+a25 wz[t]}
ww={wz[0]==w0,alpha[0]==alpha0}

aa=DSolve[Flatten[{qq,ww}],{wz[t],alpha[t]},t]

Plot[wz[t]/.aa,{t,0,tt}]

Plot[alpha[t]/.aa,{t,0,tt}]