Amp for Soliloquy 5.3i floor standing speaker?

The Soliloquy 5.3's do not like tubes in the power department. The preamp department will be fine with tubes but you have to have an amp that can control the woofers or bass. I read so many opinions of them sounding good with tubes. Not so! They were truly fat in the bottom end and bloated. The top end was rolled off no matter what tube amp I used under 50 watts. They sound better with good solid state. I had very good luck with a Odyssey Stratos power amp, Older PS Audio Elite integrated , Adcom 535 MkII, and Parasound ( I don't remember the model but it was 100 watts.) The Odyssey Stratos by Odyssey Audio was the best combination we got out of them. Be careful not to blow the woofers they are hard to find. They actually don't exist on the market. The gentleman I purchased mine from drove his with Rotel gear but I never heard it personally.
I suggest that you get as much power and quality that you can afford for them. There are some interesting hybrids with more power out there but you will pay through the nose for most of them. Good Luck

The Soliloquy 5.3's do not like tubes in the power department.

My experience would entirely contradict that statement. I've owned 5.3i's and have helped two friend's build systems around them. They're great speakers for the money and it's a shame they went out of business. If you wanted to stick with Jolida two of the friends who have had them used Jolida 502B amps and I thought that combination was very good. Another excellent choice I've heard extensively is with the Unison Unico hybrid integrated. I used mine with separates. The best combination I found with them was with Quicksilver Mini-mites and in a small room with Wright Mono 10's (they sounded astoundingly good with those amps - but I would not try that combo in a larger room where you may need more power).

PS The friend I sold my 5.3i's to had a Jolida 1501RC that he brought to my house to try them out with. I did not like that combination at all. I found it rather harsh and unrefined (in my room with the rest of my system and starting out from dead cold). I later heard the combo in his house with the amp a bit warmer and with more space around the speakers. Though it sounded better there, I'd still strongly point to the recommendations above for a big improvement in what I heard of that combination.

I'd start by looking at Cary amps as they were developed with them.

Kal