The circles  $x^2+y^2-10x+16=0$ and $x^2+y^2=r^2$ intersect each other in two distinct points if

Centres of the given circles are $C_1(5,0)$ and $C_2(0,0)$ and their radii are $r_1=3$ and $r_2=r$ respectively. For the circles to intersect at two distinct points, we must have 

$\begin{array}{l}\left|r_1-r_2\right|<C_1{C}_2<r_1+r_2\\ \Rightarrow r-3<5<r+3\\ \Rightarrow r<8\text{ and }r>2\Rightarrow 2<r<8.\end{array}$