Hello,
I bought some bitcoin on Coinbase. Can I send them now to the desktop wallet of bitcoin.org, and leave it there for 5 years or longer, without caring about it in this timeframe? Or is it neccessary to update the wallet from time to time? What happens when Litghting-Network or a fork is coming, do we have to update something?
No, under normal circumstances there shouldn't be any problem storing them for whatever timeframe you have in mind.
Even if bitcoin forks/if there's a critical update ( something like segwit), there will always backwards compatibility/ opt-in ( like segwit, you don't necessarily have to use it).
In the case of a fork you might indeed need to download another wallet to access the funds/coin you received from the fork, ( See bitcoin cash wallets etc), but there shouldn't be any problems with the bitcoin wallet.
Unless there is a critical vulnerability found in ( the then older versions of ) bitcoin core ( See what happend to electrum), then it of course might be smart to update it before sending / receiving any bitcoin with it.
In rare circumstances i could see that certain payscripts which bitcoin core currently uses will be invalid in the future/not accepted by most nodes, but then again just update your wallet and you should be able to make a transaction with your bitcoins just fine.