I'll be traveling in Europe and don't want to be bothered by incoming calls that would be outrageously expensive. Is there a way that I can block them on my S5?
You can also try apps like RCB (remote call block) but most require root. Leaving your phone in airplane mode as has already been suggested would be the best option
As Rukbat said, aeroplane mode is the best way and you can switch WiFi on & off when you need it. Also, in most countries buying a prepaid SIM card is very cheap and you can use it for local calls or mobile data. For example, right now I'm in Spain using one. Free sim card and 5 euros for 500Mb. More than enough to use with online messages and calls.