How can the distance from an observer to a lightning flash be estimated, and can anyone explain how this works and provide an example?

Because sound travels more slowly than light, thunder is heard after the lightning is seen. The distance between an observer and the lightning bolt can be estimated by counting the number of seconds between the lightning and the thunder. The light reaches the observer almost instantaneously, but the sound travels at about 1.6 km (about 1 mi) every 5 seconds. Thunder can seldom be heard from more than 24 km (15 mi) away.

https://www.livescience.com/37734-how-far-away-is-lightning-distance.html

The time between seeing a lightning flash and hearing the thunder it produces is a rough guide to how far away the lightning was. Normally, thunder can be heard up to 10 miles from the lightning that makes it. Lightning heats the air around it to as much as 60,000 degrees, producing sound waves by the quick expansion of the heated air. Since light travels at 186,000 miles per second, you see the lightning the instant it flashes. But sound, including thunder, travels about a mile in five seconds near the ground. If 15 seconds elapse between seeing a lightning bolt and hearing its thunder, the lightning was about three miles away. Lightning closer than about three miles away is a warning to take shelter immediately. Successive lighting strikes are often two to three miles apart. If the first stroke is three miles away, the next one could hit you.

https://www.weather.gov/safety/lightning-science-thunder
educ.uvic.ca/Faculty/mroth/438/LIGHTENING/web%20stuff/distance.html no longer exists

The distance can be estimated by the observer:
1.) Noting the exact time of the flash
2.) noting the exact time that the sound of thunder reaches the observer.

Since the speed of light in a vacume is 186,282.397 miles per second. In our normal atmosphere, between 10,000 feet and sea level the speed is just a tad less, about 186,024.739 miles per second.

Since the speed of sound at sealevel is .2114 miles per second.

All you have to do is to take the fime lag of the sound being observed after the flash, calculate the distance that it would take sound from the flash to go in that length of time. Calculations using these two vectors can give you an exact value,

But to get an appooximation, just figure for every second of lag time of the sound of thunder longer than the flash is about 1/5th of a mile.

Thus a lag time of 5 seconds = one mile. ( it would really be one and 1/20th of a mile.)

Professor D. L. Dillinger