You can get a freewheel with bigger cog or find a crank with a smaller ring for the front. Or possibly change that ring to a smaller one.

Finding an old bike repair shop that is amicable to the idea of re-using old parts they have laying around since that bike was new might get you fixed up cheaper than looking around to buy new stuff.

Personally, I wouldn't go to the extent and expense of putting a double on it for what your stated use is going to be.

If you were not aware of it being five speed, then are you certain it was shifting through all the gears to the big sprocket?