Which LS3/5a?

I have extensive experience with the Rogers and would not consider any other make. If you can find a pair in good shape by all means go for it. On stands with a pair of subwoofers and a properly treated room you can have a 90% system. The last 10% will cost you $100K. 

The new Roger’s “special edition” aka gold badge are by far the best (and most $$$). Try listening to all of them. The chartwell’s /vintage sell for the most because their vintage, but of the new ls3/5a’s the Roger’s se’s take the cake! Add an audio research i50, and you have as close to “perfection” as $$$ can get! (Or an allnic T-2000) but they’re $15,,000! Since they’re 15 ohm and have a slightly crisp sound, you definitely want to pair them with a high-quality tube amp. 

the ls3/5a's are indeed iconic speakers, but i would say in the present day there are many many more cost effective and better sounding mini monitors out there... so unless there is a nostalgia/classicism motivation here, i would go with little proacs, harbeths, vivids etc etc

I had chartwell Ls3/5as over 40 years ago and they were wonderful for their time.

I can't help wondering if their are better options today (I'd check out LSAs offerings) but if you want Ls3/5as here is a review of 4 different ones: