About the only thing you can't transfer, and the only thing that matters, is the SIM-card number itself. And that's what the carrier uses. Calls don't go to your phone number, the carrier receives them, looks up your SIM-card number, and sends the calls to that. Most carriers won't use a generic SIM shipped with a phone. If you bought the phone from your carrier, it will have their SIM card in it, and it will be activated (and your S5 will no longer make phone calls). If not, you'll have to get a SIM card from your carrier (or MVNO [Straight Talk, Mint, etc.] if you're not using a carrier) and call them when it's in the Note 8 so they can switch the account from the old one to the new one. (I wouldn't advise trying to cut the card - it can be done, but if you do it wrong you're "phone-less" until you get a card for the Note 8.)
Cards now come in "universal.size". If you break the largest part of the card out of the credit-card size card it's part of, you get an old fashioned (and probably not used any more, unless you have a really old phone) full-size card. If you break off the larger of the "smaller" card piece, you get a micro-SIM. If you break off the smallest part, you get a nano-SIM. (It's cheaper and easier for the carriers to only have to carry one kind of card. When we switched from 32MB to 64MB cards [back around 2004], we went nuts if we dropped a mixed handful, reading card numbers against spreadsheet lists of deliveries. - We had to check every single card. I don't know why I didn't think of just putting an S [for "six"] in a corner of the 64MB cards. Many customers didn't need the larger cards, but they knew that they existed, so putting 32 and 64 on the cards would have meant a store-full of 32 MB cards.)