Yes there is a way to do that. It is done by scripts and a smart contract, script feeds the address list to smart contract in bulk packages, and smart contract sends them with the standard send command (looped).
The avarage cost of airdropping tokens is 0.1ETH per 1000 addresses ( I'm talking about gas cost only ). So for your examplary 5000 addresses, you'dpay 0.5ETH gas fee.
I now understand why some projects say they are giving airdrops yet end up asking for some ether in return. This is just for them to cover the cost (gas).
That along with the fact that some of those people never plan to airdrop a token and just want to get a little bit of money from everybody before running away. The utmost low scam of scams, but hey you know somebody out there is going to attempt it.