We can use the formula for the distance between two points in a plane to find the magnitude of the vector v-w:
||v-w|| = √[(v1-w1)^2 + (v2-w2)^2]
where v1 and v2 are the x and y components of vector v, and w1 and w2 are the x and y components of vector w.
Using the given values for v and w, we get:
v1 = 5, v2 = -2
w1 = -4, w2 = 3
Substituting these values into the formula, we get:
||v-w|| = √[(5-(-4))^2 + (-2-3)^2]
||v-w|| = √[(9)^2 + (-5)^2]
||v-w|| = √[81 + 25]
||v-w|| = √106
Therefore, the magnitude of the vector v-w is √106.