Average Rounds of Combat in 5e

The number of combat rounds has a strong influcence on how costly it is to use an action, for example a spell that produces an effect for a minute, enough to last the whole fight: if the fight only takes three rounds, you will only benefit from it for two rounds. If the fight however takes eight rounds, you get seven rounds of benefit. 

Three rounds is assumed to be standard, because the DMG in the monster building rules (page 278) tells us:

If a monster's damage output varies from round to round, calculate its damage output each round for the first three rounds of combat, and take the average

And on p.281, in the Monster Features section for factoring Regeneration in CR calculations:

Increase the monster's effective hit points by 3 x the number of hit points the monster regenerates each round. 

Both indicate that the game seems to expect combat to take three rounds. 

More importantly, this length is also supported by the amount of damage characters deal against the hit points of a an appropriate monster: a group of four would reduce such a monster to 0 hits in about three rounds.  

A higher end of five rounds is based on empirical data at one specific table.

You often do not attack every round in every fight when you spending time to manoever or take cover, so the fight duration in rounds might increase, but the number of rounds where you fully attack may not. This would make for longer combat, but in a way that is not material for resource use math. 

In my experience, larger and more deadly battles take longer, sometimes much longer, as opponents not only move around and jockey for cover, but as there are many more opponents and hit points to grind down, while small fights or fights against weaker opponents are over even faster. 

In reality you will tend to have fewer, deadlier encounters than the DMG guidance suggests. Instead of 5 or so medium combats, you end up with only three deadly ones per day, sometimes even only a single really huge monster-ball battle. This will lead to longer combat in the wild than what the DMG math implies. 

For these reasons, I think four rounds per combat encounter is a better average than three.