The bike, in the condition your describe, is probably worth $600 - $900. If you want to go modern, sell it and go on down the road.
I think your bike can be found in this brochure.
http://www.vintage-trek.com/images/t...rekTouring.pdf
It lists a 5 speed rear freewheel with Heliomatic hubs. Those are unique hubs, but generally good. I would surmise that, if it has sat for 20 years, you've probably got low grade varnish in those hubs. Clean out the grease and bearings in the wheels with a good solvent and have them tuned up and lubed with some new product. Freewheels vanished for 7 speeds and beyond because it put the bearing inboard of the right chainstay to the extent that you could bend the axle with some heavy torquing. I toured for a long time on 7 gears in back with a 14-34.
A 32 tooth top gear can save you a lot of sweat. You can still find freewheels here.
http://sheldonbrown.com/harris/freewheels.html
27" tires? No problems. Plenty of those around.
http://sheldonbrown.com/harris/tires/630.html
Even if the tires LOOK good, they've had the atmosphere attacking them for 25 years. Get some new ones, tubes also, before something goes POW while you're doing 20+ on a downhill.
A couple of years ago I rode across Oklahoma with a guy who had six gears on a 1980 something Peugot.
The bike looks good. Ride it and enjoy. Or sell it to me.