Answer: The graph is shown below.
Step-by-step explanation
The given piecewise function breaks down into these statements
f(x) = 5 when x = -5 or x < -5
OR
f(x) = -x+14 when x > 5
We'll have a fairly big gap between the two disconnected pieces since f(x) is undefined when -5 < x ≤ 5
The function f(x) = 5 is the same as y = 5. It's a horizontal line through 5 on the y axis. Two points on this piece are (-6,5) and (-5,5). We erase the portion to the right of x = -5 because of the domain restriction.
Meanwhile, the portion f(x) = -x+14 is graphed when x > 5. Two points on this piece are (6,8) and (7,7). So we'll graph out y = -x+14 like normal, but erase the portion to the left of x = 5. Make sure there's an open hole at (5,9) on this second piece because x = 5 isn't defined here.
Refer to the piecewise graph below to see what I mean.
I've color coded the pieces. That step is optional. I used GeoGebra to make the graph.