This app was mentioned in 3 comments, with an average of 1.33 upvotes
To explain. What you want is called (carrier) unlocking. This will free you up from your carrier, and be able to use any SIM from any carrier in your phone. HOWEVER, the radio channels of the phone may dictate what carriers and where you may connect. For example if you have a CDMA phone, you will not be able to connect to a European carrier (who mostly use different GSM frequencies than in North America). I am quite sure your S5 will be able to connect into several carriers, perhaps all. I know that minimally it is at least a quad band GSM phone, maybe CDMA also.
In fact, I unlocked my S2 before changing the ROM. When I changed the ROM, it became carrier locked again (WTF?). I used GalaxSIMUnlock to test and unlock the phone. Did not see if root was needed for it to work. Probably many phone service places -- private, not big Tele -- will unlock it for about $25.
GalaxSim Unlock. Haven't used this app since I used it on my Note 1 so I don't know if it will work on your Note 3.
Did you try using this? : https://play.google.com/store/apps/details?id=com.spocky.galaxsimunlock&hl=en