Given information:
- Point A is located at coordinates (2,3).
- The equation of the line parallel to x-y=5 is given as 2x+y-6=0.

Steps to find the distance:

Step 1: Find the coordinates of the point on the line x-y=5 that is parallel to point A.
To find the coordinates of the point on the line x-y=5 that is parallel to point A, we need to consider the slope of the line x-y=5.
The given line can be rearranged in the slope-intercept form (y = mx + c) by adding y to both sides:
x - y = 5
-y = -x + 5
y = x - 5

From this equation, we can observe that the slope of the line is 1 (as the coefficient of x is 1).
Since the line parallel to x-y=5 should have the same slope, the equation of the parallel line passing through point A can be written as:
y = x - c

To find the value of c, we substitute the coordinates of point A (2,3) into the equation:
3 = 2 - c
c = 2 - 3
c = -1

So, the equation of the line parallel to x-y=5 passing through point A is y = x - 1.

Step 2: Find the intersection point of the two lines.
To find the intersection point of the lines 2x+y-6=0 and y=x-1, we can solve the system of equations formed by these two lines.
Substituting the value of y from the second equation into the first equation, we get:
2x + (x - 1) - 6 = 0
3x - 7 = 0
3x = 7
x = 7/3

Substituting this value of x into the second equation, we can find the value of y:
y = 7/3 - 1
y = 7/3 - 3/3
y = 4/3

So, the intersection point of the two lines is (7/3, 4/3).

Step 3: Find the distance between point A and the intersection point.
To find the distance between point A and the intersection point, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of point A (2,3) and the intersection point (7/3, 4/3) into the distance formula, we get:
Distance = sqrt((7/3 - 2)^2 + (4/3 - 3)^2)
Distance = sqrt((7/3 - 6/3)^2 + (4/3 - 9/3)^2)
Distance = sqrt((1/3)^2 + (-5/3)^2)
Distance = sqrt(1/9 + 25/9)
Distance = sqrt(26/9)
Distance = sqrt(26)/3

Therefore, the distance of point A(2,3) measured parallel to the line x-y=5 from the line 2x+y-6=0 is sqrt(