In many countries in the eurozone, shops tend to post signs along the lines of “we refuse banknotes larger than €100” for various reasons so in that sense, €500 would indeed not be well accepted. They are however still perfectly valid, even as the ECB announced it would stop issuing new ones.
In general private banks should therefore have no problem with it but might not necessarily offer cash services to non-customers. If nothing else works, you should however be able to exchange them at one of the branches of the Banco de España.
No matter what you do, if you want to change a large amount of cash, you might have to present ID or satisfy some other reporting requirement.