LS3/5a are not difficult speakers to drive and you don't need a lot of watts to get reasonable listening levels in an average room. I've driven them with amps, both tube and ss, from 15 watts to 140 watts per channel.
Presently, my best results are with a restored vintage Quad 405-2 with a Quad tube preamp. Completely silent at idle, as long as I correctly keep power cords away from interconnect cords at the back.
More important, I think, is the character of the amp. The ls3/5a need a lusher kind of amplification to mine the tonal richness available, and to fatten instrumental timbres. I used class D for a few years, but the top end can become brittle and dry. I would also avoid passive preamps. An active preamp adds good body to the tones.
So, vintage, perhaps?