There's no set rule for how much to feed a horse because horses all have different rates of metabolism. It has very little nutritional value, so it's not like fortified grain or a ration balancer where there's a minimum amount you need to feed in order to supply the horse with enough vitamins/minerals. For weight gain, you usually start off with a small amount (maybe 1-2 lbs, measured dry) and increase or decrease until you're seeing the results you want.
If you're feeding it to replace hay, you'd want to replace an equivalent amount based on digestible energy, not by weight. As its lbs not miles mentioned, beet pulp is higher in DE, so you'd replace 5 lbs of grass hay with ~3.5-4 lbs of beet pulp.