If you can get that bike up to 30 mph on any reasonably flat road, you are a strong rider indeed. Given your gearing, that requires a cadence of 105 rpm and given the riding position, it requires pretty impressive wattage.

It is theoretically possible to regear this bike with a larger chainring say 52T in place of the 48T. A higher geared freewheel could also be used. An Ultra-6 13x28 used to be available from Sun Tour that's a direct replacement for your 5-speed and, depending on your dropout spacing, perhaps a 6 or 7-speed freewheel could be used.

However, economically it's isn't worth it. The bike is really obsolete and was a low line model to begin with so you will run into the "silk purse from a sow's ear" problem very quickly. If you change the freewheel and chainring, at the least you will ned a new chain and the "improvements" will get expensive rapidly, particularly if you have to pay a dealer to provide and install the parts.

Take the money you would spend on this bike and apply it to one that's newer and better suited to you needs.