Starship has a return capacity of 50 tons.[0] If you have 5000 tons of material to return, that's a hundred Starship flights.
I wouldn't expect asteroid mining to be viable until we have Starship or something like it at scale, doing thousands of launches per year. If most of those flights return empty, then that's a lot of cargo space already available.
Starship uses $1 million in fuel to launch 100 tons to LEO, so half that much should be plenty to take 50 tons back down. But Starship's propellant mass for launch is 2600 tons[1] so that'd be up to thirteen launches to put the landing fuel in orbit. Actually it'd be less, since a lot of the orbital velocity is burned off by atmospheric breaking, not sure how much.
Ideally though, get the fuel from the same asteroids you're mining already. Starship uses methane, so you're just looking for water ice and carbon, both abundant in asteroids.
At current prices, 5000 tons of gold is worth about $400 billion, so it's not obvious that this wouldn't be economical. The world mines about 3000 tons of gold annually and the price of gold has still been going up, so if our asteroid miner returns a couple thousand tons per year it might not crash the price too badly.
Gold is the worst example because the price of gold is almost 100% based on its scarcity. Doubling the supply of gold would just cause the price to roughly halve. Hilariously, if you actually had the capability to inundate the world with gold, you'd find it much easier and still extremely profitable to extort the people who own gold to pay you not do so.
You'd make a lot of money on the way to doubling the world's supply. 3000 tons annually just doubles how much we mine, not how much we have; that's more like 190,000 tons. And even if you doubled the total supply instantly, you'd now own half the current value of the world's gold, which would be about $6 trillion.
And of course gold has all sorts of really useful properties, so long term, it'd be worthwhile to make it abundant and cheap.
I wouldn't expect asteroid mining to be viable until we have Starship or something like it at scale, doing thousands of launches per year. If most of those flights return empty, then that's a lot of cargo space already available.
Starship uses $1 million in fuel to launch 100 tons to LEO, so half that much should be plenty to take 50 tons back down. But Starship's propellant mass for launch is 2600 tons[1] so that'd be up to thirteen launches to put the landing fuel in orbit. Actually it'd be less, since a lot of the orbital velocity is burned off by atmospheric breaking, not sure how much.
Ideally though, get the fuel from the same asteroids you're mining already. Starship uses methane, so you're just looking for water ice and carbon, both abundant in asteroids.
At current prices, 5000 tons of gold is worth about $400 billion, so it's not obvious that this wouldn't be economical. The world mines about 3000 tons of gold annually and the price of gold has still been going up, so if our asteroid miner returns a couple thousand tons per year it might not crash the price too badly.
[0] https://space.skyrocket.de/doc_lau/super-heavy-starship.htm
[1] https://en.wikipedia.org/wiki/SpaceX_Starship