Sounds like they just wanted to fire you and used the late excuse. I mean, five minutes? How many work places have you worked in where A LOT of people weren't walking in the door 5-10 minutes late every day? Especially in non-customer facing postions.
Plus, you're the only IT guy on site? Even if you were late, if you were doing the job, they would've kept you simply because they had no other choice. What company throws away an IT person who's familiar with their system without having others in line?
For some reason, they just wanted to get rid of you.
Peace