Draw the asymptotes first. To find them solve x²/5-y²/2=0, (x√0.4+y)(x√0.4-y)=0.
The two asymptote lines are y=-x√0.4 and y=x√0.4.
Then put y=0 to find the x intercepts, which are x=-√5 and x=√5.
The hyperbola can now be drawn so that it passes through (-√5,0) and (√5,0) and is trapped between the asymptote lines on either side of the origin.
Before rotation: