I'm nearly 80 and began cycling about 7 years ago. I began as you have riding 5 miles then 10 etc. Bit by bit I got to 30 miles and then signed up for a 50 mile cancer fund raiser. I continued increasing miles adding 10% mileage increases, as recommended by the people who study these things. I did that ride and from that point forward 50 to 60 miles became a typical ride.
I was not very comfortable on the bike at first. Many aches distributed all over. I've messed with my fit on the bike, been through a number of different saddles (about 6 I think) and the bike feels good. The longest ride has been 72 miles and I ride 3000 miles a year. If you keep doing what you are now doing, you will get up to, what now may seem to be astonishing distances. Once you get to those astonishing distances, especially for older riders, you will need be be familiar with the recovery process. Google "sports recovery" and the many and videos on this topic.