Precalculus, Chapter 10, 10.1, Section 10.1, Problem 63

Take note that the formula to determine the distance from a point (x_o, y_o) to a line Ax+By+C=0 is:
d = |Ax_o + By_o +C|/sqrt(A^2+B^2)
To apply, set one side of the given equation equal to zero.
y=-x+5
x+y-5=0
Then, plug-in the coefficients of x and y, as well as the constant to the formula.
d=|1x_o + 1y_o + (-5)|/sqrt(1^2+1^2)
d=|x_o + y_o - 5|/sqrt2
And, plug-in the given point (-2,6).
d=|-2 + 6 - 5|/sqrt2
d=|-1|/sqrt2
d=1/sqrt2
d=1/sqrt2*sqrt2/sqrt2
d=sqrt2/2
Therefore, the distance between the point (-2,6) and the line y=-x+5 is sqrt2/2 units.