Answer
$ (x-2)^2+(y+4)^2=25$
See graph.
Work Step by Step
Step 1. Transform the equation $x^2+y^2-4x+8y-5=0 \Longrightarrow x^2-4x+4+y^2+8y+16=5+4+16 \Longrightarrow (x-2)^2+(y+4)^2=25$, thus it is a circle with center $(2,-4)$, radius $r=5$
Step 2. See graph.