+1 on replacing the tires. Five years is getting to the end of the useful life of motorcycle tires and I don't know why bici tires would be any different. You want them to stick to the road when you're trying to corner and brake, and tread compounds harden as they age.
You'll probably want fresh grease in the bearings (headset, bottom bracket, hubs, pedal spindles). I'm not sure how long that lasts, but if you never re-packed your bearings before, the grease is now 10 years old, and it's due.
Speed comes from what you put behind you. - Judi Ketteler