To use your Note 5 in Europe, you will first need to check that it is not 'locked'. Domestic carriers (ie the phone company that sold you the phone) lock their handset so that it can only be used on that country's network and only with that SIM. So you'll need to check that first, and there may be a fee to get the lock removed. Once that is done, however, you can use any SIM you like, anywhere you like.
For the very cheapest rates, I'd go for a local SIM card for each European country you're visiting. This will save you the most money, but not the most time. You will have to find the right store, make sure you've got the right plan and wait to be registered, all of which will take up time you may want to spend doing other stuff. So an International SIM card makes a lot of sense, especially if you're travelling to more than one country. I've used the Telestial European SIM card before, which offers the same rates for most European countries, plus reduced calling back to several other destinations, including the USA, Australia and South Africa. The most expensive and dangerous method is to roam on your domestic plan. These rates tend to be the most expensive, and unless you're monitoring your usage like a hawk, the first you'll know about it will be when you receive your monthly bill.
Hope you have a great trip!