7.1 or 5.1

Your dealer gets to sell you an extra pair of speakers.

A 7.1 channel system incorporates all the elements of a 5.1 channel system, but instead of combining both surround and rear channel effects into two channels, a 7.1 system splits the surround and rear channel information into four channels.

In other words, side sound effects and ambience are directed to left and right surround channels, and the rear sound effects and ambience are directed to two rear or back channels. In this set-up the surround speakers are set to the side of the listening position and the rear or back channels are placed behind the listener.

One simple benefit is that it can provide a more immersive experience. Like when a live audience applauds at the end of a performance, some clapping comes from the rear, helping to create the impression that you are in the performance hall.

During the performance, some echo might be audible from the rear, suggesting that you are in a large hall and some sound is reflecting off the back wall.

And of course for movies, the back channels offer the opportunity for sounds from behind, like explosions or the snap of a twig as someone approaches you from behind.

You may want to post this question in the Home Theater forum as you'll get more responses.

Since this is the Analog room my answer is, why would you want more than 2 channels? Let alone 5 or 7?