Cat5e cables in Wall never connected to jack

Hello r/HomeNetworking! We purchased a house here in Ireland a few months ago, it's a recent enough build from 2016 but there was no sign of it being wired for Ethernet, only a few coax ports ending in the living room, a dining/TV room and upstairs in the main bedroom. Today I finally got around to checking some the loose cables and to my surprise there was the end of a Cat5e cable in the living room conveniently located near my internet router. I then find another one near the the coax end in the bedroom that was hiding being a painted panel... I have a couple of questions now before I see if I can finish the job myself.

• The two cables I have found are different colours but clearly identified as Cat5e, would they likely have been crimped with one another or would that be pretty unusual and there could be an extra terminaison somewhere else?
• Is the only way to see if there's continuity between the two cables to finish the cable with a socket or a jack?

Thanks a lot in advance for any hints or advice to how I could investigate this more!