There are three possibilities:

A. The point on the line that is closest to (1,3) is greater than five units from (1,3). In this case, there are no points satisfying your criterion.

B. The point on the line that is closest to (1,3) is exactly five units from (1,3). In this case, there is exactly one point satisfying your criterion.

C. The point on the line that is closest to (1,3) is less than five units from (1,3). In this case, there are exactly two points satisfying your criterion.

You could try to find the point on the line closest to (1,3), but I claim that's more work than you need to do. If you plot the point and the line, you can see at a glance that the point (1,1) is on the line. What is the distance from (1,1) to (1,3)? What does that say about the distance from (1,3) to the point on the line closest to (1,3)? So which case are we in?