Question 112353
First, find the line perpendicular to your original line that goes through the point (5,3). 
Perpendicular lines have slopes that follow this relationship,
{{{m[1]m[2]=-1}}}
Their slopes are negative reciprocals.
Your original line slope is 4. 
Your perpendicular line slope is then (-1/4).
Using the point-slope form of the line, your perpendicular line is,
{{{y-y[1]=m(x-x[1])}}}
{{{y-3=(-1/4)(x-5)}}}
{{{y=(-1/4)x+5/4+3}}}
{{{y=(-1/4)x+5/4+12/4}}}
{{{y=(-1/4)x+17/4}}}
{{{ graph( 300, 300, -10, 10, -10, 10, 4x+1, (-1/4)x+17/4) }}} 
Now that you have the equation for the two lines, you can find the intersection point where the two lines meet. 
From there you can calculate the distance from the intersection point to (5,3) to get the final answer.
1.{{{y = 4x+1}}}
2.{{{y=(-1/4)x+17/4}}}
Substitute equation 1 into equation 2 and solve for x.
2.{{{y=(-1/4)x+17/4}}}
{{{4x+1=(-1/4)x+17/4}}}
{{{(16/4)x+(1/4)x=17/4-1}}}
{{{(17/4)x=17/4-4/4}}}
{{{(17/4)x=13/4}}}
{{{x=13/17}}}
From 1,
1.{{{y = 4x+1}}}
{{{y = 4(13/17)+1}}}
{{{y = 52/17+17/17}}}
{{{y = 69/17}}}
Now you have found the intersection point.
Use the distance formula to find the distance between the intersection point and the point (5,3)
{{{D^2=(x[1]-x[2])^2+(y[1]-y[2])^2}}}
{{{D^2=(13/17-5)^2+(69/17-3)^2}}}
{{{D^2=(13/17-85/17)^2+(69/17-51/17)^2}}}
{{{D^2=(-72/17)^2+(18/17)^2}}}
{{{D^2=(5184/289)+(324/289)}}}
{{{D^2=(5508/289)}}}
{{{D^2=(5508/289)}}}
{{{D=4.37}}}