We are given linear function h(x) = –x + 5.
On comparing with slope-intercept form y = mx+b, we get b=5.
Therefore, y-intercept is at 5.
We need to change to move the graph down 3 units.
According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.
Therefore, in order to move the graph down 3 units, we need to subtract given function by 3, we get
y = -x+5 -3
y = -x +2.
Here y-intercept is 2.
Therefore, correct option is 3rd option: the value of b to 2.