Hi OverseasTrav and welcome to bytes.com!
Whether your phone will work overseas depends on a few factors; basically what you have to know is:
- Which version of the Nexus 5 do you have? (The D820 or the D821)
- Which network bands are used in the country you are going to travel to?
You can read up on the differences between the models and the bands they support
here.
Whether you'll have to change your plan and what additional charges you may face depends on your carrier and plan; it's probably easiest to ask them that question. Be sure to mention where you'll be going, how long you'll be there and which services you'll want to be able to use (phone calls, text messages, internet access).
Another hint: When WiFi is an option (e.g. in hotels, cafés, at conferences, etc.) that will in many cases be both cheaper and faster than using, say, LTE. Whether it's the better option for you depends on what you want to do with the connection and what the conditions would be like without WiFi.