How do you graph f(x)= |x-2|+5

For this we are going to use the equation f(x)=a|x+h|+k
Since there is no a shown, we know that a=1. This means the slope of the graph by 1's. (slope=1 one on the right side and slope=-1 on the left, because absolute value graphs are shaped like a "v".)
Since h=-2, just move the function to the left 2 units.
Since k=5, move the function up 5 units.
This basically means the vertex of the function is at the point (-2,5).

So put the point (-2,5) on your graph, then make the v-shape with a slope of 1 on the right side, and -1 on the left. 

Sometimes if you aren't sure how the graph will look, just plug x-values into the function to get their corresponding y-values. Then see how the graph looks to check.