I work in the material handling industry. 5,000 lb electrics use a pretty decent sized battery. I would say $5,000 would be on the low end for a new battery of this size. The last I sold was pushing $8,000 and that was a new tubular lead acid 48v/765 Ah with a 5 plus 1 year warranty. I've priced some out that were close to $10,000. Really depends on the model and your requirements. Multi shift/opportunity charging requires a more stout battery then a light single shift. Some trucks have multiple sized battery boxes available in the same model. Allows for larger capacity (longer) batteries. The data plate on the truck should list the voltage, box size, and minimum weight for the battery.
Check around with your local forklift dealer as most of them sell multiple brand batteries. Sometimes the battery OEM's have demo batteries available for significantly less cost. These batteries might have a few months or a year use on them. They usually sell with a much shorter warranty but might be half the price. The ones I've looked at will guarantee at least 80% capacity of new. Also check if any dealers offer refurbishing services. Sometimes it might be a bad cell that needs to be replaced. If the battery is old and hasn't been taken care of then it might not be worth putting money into.