I'd check all the silly stuff Ellie, loose fuses, relays etc in the fuse box. For example, a couple of weeks back mine gave the impression of running out of petrol. I knew it wasn't as i'd filled up the previous day.
I couldn't hear the fuel pump running when it should though. Checked the fuses and the fuel pump fuse was loose.
Pushed it back in properly and away it went.
It sounds as if you're momentarily losing power to the alarm system so it's having a funny five minutes so worth a look especially for the amount of time it takes.
