Question 738201
This would be difficult to use the system to show a drawing and graph, but I am handling it like:


The line x=3, y=infinity, 
A segment with endpoint at (5,3) and perpendicular to the line x=3, will be seen to intersect the line x=3 AT the point (3, 3).  

EITHER of two points are also on the line x=3, and each of these is {{{sqrt(5)}}} from the point (5, 3), but we do not yet know the y coordinate for this point.  
... BUT we DO have a triangle, actually a  RIGHT triangle and we can find the length up or down from point (3, 3) using pythagorean theorem.


From (3, 3) to (5, 3) is 2 units.
From (5, 3) to (3, u) is {{{sqrt(5)}}} units.  
From (3, u) to (3, 3) is h
Let's find h using pythagorean theorem.

{{{h^2+2^2=(sqrt(5))^2}}}
{{{highlight(h=1)}}}
Therefore, u=3-1, {{{u=2}}}.
ANSWER: The coordinate pair for the specified point is then either (3, 2) or (3, 4).