Updates:

Rotation direction for complex roots: look at original matrix, since b= -5 <0 and c=1>0, so it is counterclockwise.

When the real part is positive, spiral outward, unstable; when the real part is negative, spiral inward, stable.

when $\alpha$ = $\sqrt{20}$ (it's positive, outward, unstable)

It is in repeated root case, but only has one independent eigenvector, therefore, we could graph in the direction of this eigenvector, following the direction of counterclockwise as the same for complex roots.

Similar for $\alpha$ = $-\sqrt{20}$, it's negative, inward, stable, counterclockwise still.