Question 971021
You would be looking for EXACTLY one point of intersection.  If two points of intersection, neither would be a point of tangency.


{{{x^2+(mx+5)^2=5}}}
{{{x^2+m^2x^2+10mx+25=5}}}
{{{(1+m^2)x^2+10mx+20=5}}}


The rest might be messy, but you want the discriminant to be ZERO.  The single variable will be m and you just....(?)  solve for m using the discriminant.