Ayre V-5xe best tube pre-amp to match with?

The K5xe is an excellent solid state preamp at its price level. However, they're better to be had in the tube arena. The Ayre K1xe is an excellent preamp anyway you want to slice it but very expensive. If you have the money, it mates superbly.
I agree with the BAT 51se recommendation also. Good match.

I don't have, but have heard Ayre amps paired very nicely with VTL tube preamps. Very musical combo. The VTL 7.5 is amazing, but very pricey; believe the new 6.5 or even the 5.5 might be a match.

Frankpiet, I thought of going with an Ayre pre with my V-5xe, but wanted tubes in the chain. After a ton of research I went with the BAT VK51-SE. If you don't mind the price of the BAT, I think it's as close to a perfect match as you could ask for. The venerable Mr. Bigtee and I both found that certain tube preamps will cause a 'hum' when matched with the Ayre. I would highly recommend BAT or try a home demo if you go with another brand.. or check with Ayre to avoid a compatibility issue. Btw, you might check TAS review of the 51SE. The reviewer gave a slight edge (in his opinion) to the BAT when compared to Ayres K1-xe. ..good luck

Bigtee / Classical1: which tube pre´s caused a hum when connected to the V-5xe ?
I´m not familiar with the BAT hause sound, but I´ve heard the best value pre from BAT is the VK 31 SE - is this a good one? I´ve also heard Aesthetix Calypso, CAT SL-1 and Modwright SWL 9.0 SE would be a good match ?

Whatever choice you make get a truly differential balanced preamp. The Ayre gear is meant to be run with a balanced signal and although it sounds okay single-ended balanced is the way to go. The mere presence of XLR outputs on the preamp does not necessarily imply a balanced signal. Atma-Sphere, Audio Research and BAT are balanced and I believe Aesthetix is too. CAT, ModWright, Herron and (most- perhaps all) VTL are single-ended.
Ultimately there are better preamps than the K-5xe or K-3x but within their price range I haven't heard a preamp that is absolutely better. The affordable tube preamps are more different than better in any absolute sense.