jmc

Because the foci both lie on the line $x=5$ and the center of the hyperbola is the midpoint of the segment connecting the foci, the center must also lie on the line $x=5.$ However, we also know that the asymptotes of the hyperbola intersect at the center. Therefore, the center of the hyperbola lies on both the line $x=5$ and the line $y=3x,$ so its coordinates are $(5,15).$

Because the hyperbola has a horizontal axis, the other asymptote must have slope $-3.$ Therefore, we can write a point-slope equation for the other asymptote: $$y-15=-3(x-5),$$which is equivalent to $\boxed{y=-3x+30}.$