Any old cat5 can handle 1000BASE-T. 1000BASE-TX uses 2 pairs (4 conductors) and is pretty rare in the wild, whereas 1000BASE-T uses all 4 pairs (8 conductors). https://www.iol.unh.edu/sites/default/files/knowledgebase/ge...

This has more information on cat5 vs cat5e vs cat6 and their compatibility with different speeds / modes: http://serverfault.com/questions/107172/what-is-the-actual-d...

TL;DR almost any Ethernet cable you buy today will be cat5e or better, which will work just fine. Really old cat5 is technically compatible and should work too, but due to it having slacker tolerances for e.g. crosstalk, it might not work over e.g. longer runs or difficult situations (cable ran next to fluorescent lights, etc).

EDIT: If you want to know what speed your link-level has established, your OS should provide this info. netstat -e on windows or netstat -i on OSX / Linux should show the connection speed. In windows, you could also do WinKey+ r -> ncpa.cpl -> right-click active internet connection -> connection details IIRC.

To add on to that: 100BASE-TX and 1000BASE-T use the exact same symbol rate, 125MHz. Better cables are nice but not critical.

Cat5 is suitable even for 1000BASE-T (Gigabit), although at that speed it's just not as good as Cat5e [1]. But it should be enough to handle 120mbps.

[1]: https://en.wikipedia.org/wiki/Category_5_cable