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In the line, there will be two points which are at a distance of 5 unit from A(2,3)
If we go forward or backward  5 units in a line with slope 3/4, 

change in x-coordiante =  (\frac{4}{ \sqrt{3^{2}+4^{2}} })*5= \frac{4}{5}*5=4

change in y-coordinate =  (\frac{3}{ \sqrt{3^{2}+4^{2}} })*5= \frac{3}{5}*5=3

So if we go forward 5 units, the point will be (2+4,3+3) or (6,6)
    if we go backward 5 units, the point will be (2-4,3-3) or (-2,0)