Have you taken the car back and asked them to sort it?

Probably not or you would not be asking.

It staggers me that any person would need to ask such an obvious question.

Simple fact, one or possibly even two of those faults render it illegal to use on a public highway.

I bought a used car in August from a dealer. A number of serious faults have since arisen.

If the faults have arisen since purchase then you have much less recourse under law, once 30 days have past since the sale.

You will be relying on the "goodwill" of the dealer to put things right.

If we are talking about an original C5 bought for £1000, forget it.

If we are talking about a late model C5 for £4000, then maybe you can politely request that the selling dealer fixes the faults.

Having previously owned an early C5, I can say that the Service, ESP and ASR lights coming on is quite common and usually down to a pressure sensor or egr fault. Tracing it however, is another matter.

You need the dipped headlights fixed asap. As skidpan says, not legal.

Was the AC working when you bought it? Does it just need a re-gas (£40)? or is there a fault with the compressor or a tiny hole in the pipes?

I suspect you will end up funding most of these things yourself. Both the early and later C5s are brilliant cars when working correctly. The early ones have a poor reputation for reliability, which sadly was mostly justified.