The easiest (and least expensive) way to get that kind of weight down 5 exterior stairs is to rig it off of a forklift. You may even be able to crane it over the house and drop it down that way, but you'd want to avoid that bill if possible. It can also be purely by hand, but that would also be more costly than a forklift. You will spend multiples of what you're paying for the safe to have it moved, which is likely why you're getting a good deal on it. We generally charge landlords to remove abandoned safes.
If you're going to pay to have it professionally moved, the same people moving it should be able to give you guidance on the rest. Not a dig at you in any way, but a real estate company or property owner would be out of their minds to allow somebody to attempt to move something like that who wasn't insured. It's not uncommon for us to have to provide a certificate on jobs like this. Some want $1 million, others $2.