What is a function that has a hole at (5,7/8) and resembles the graph y=(x+2)/(x+3)?

Answer 1

Since the given y(5) = 7/8, just add a factor which produces the hole.
It will look like
y = (x+2)(x-5) / (x+3)(x-5)

everywhere except at x=5, it will give exactly the same balues as the original function, but will be undefined at x=5.