I would advise you to re-engage them online the closest way possible to how you would expect to in a real-life situation.
Sending a friend request on Facebook out of the blue to someone you are not normally in touch with can come across a little weird. When I receive a request like that it feels like the person has 'tracked me down', and if they were never a close friend it leads to wondering why, and what their motive is.
Try sending a message before a friend request. Be honest and friendly. Perhaps say:
Hey - I just noticed you come up in my feed - are you the same [name] I
went to college / worked with at [name of college / workplace] ?
Be specific about where you think you know them from, not vague. If they don't remember you and you are vague they may think you're not genuine.
And of course, be prepared for any outcome. They may not reply, or they may not add you as a friend.
If it goes well then you can make the call to either send a friend request, or just wait for them to send one.