First of all I will start by welcoming you to the forum!
easiest other way to know if you have the B&O system is, when you open your driver car door is the speaker circular? So a circle silver trim with a speaker in the middle. On the trim it should have "bang and olfusen".
Vehicle View - Audi A5 2.0 T FSI quattro Black Edition Coupe - Walton-on-Thames
(look at the bottom left of the drivers door)
Then that means you have the system. If not its just the standard system.
The b&o system is a premium sound system. Like also saying Bose. It was an optional extra for about £500/600. (I don't have a brochure in front of me to give a you an exact figure or more details on its output) this means the sound is more crisp and clear. People often get it confused with loudness. It's to offer more clarity in the sound, hear extra notes or background vocals, etc that you wouldn't normally hear on a standard sound system. The opposite to this is HD BLU RAY to standard TV or your bog standard apple headphones in comparison to premium quality ones that you pay £50+ for. Like Bose, etc
If the car is new it should be on your order invoice, if it's used/ex-demo your lucky to have this as a bonus.

usually high spec A5's come with most things, including sat nav. (especially as yours is a sport) so the previous Owner would need to add it as an extra. My car is a black edition which means it comes standard when ordering new (part of the package) how old is your car? Did you buy it new or used? If you brought it new, then it's an extra. Unless you got a package (think sound package?)
Update: just got the tech details for you;
STANDARD: 10 speakers including a sub woofer. At 180 WATTS.
BANG AND OLFUSEN: 5.1 surround sound. 10-channel amplifier and 14 speakers. Output is 505 WATTS. Also the MMI offers the owner to switch the surround sound on or off. It also offers dynamic compensation for the road noise. So the faster you go or terrain your on, the sound will automatically adjust or tweak so all you hear is the music and not the road. Even compensates if there is hail or heavy rain. (believe this function is GALA) it was a £535 extra. Standard on black edition or £600 in the sound package. This package was the B&O system with Dab radio.