Desire to try tubes

Don Sachs has started to build his first integrated, the Valhala.  Looks like another great design and is under your budget.  

"Try to get something used and vintage on the cheap and have it serviced. You don’t need to make a perfect decision on your first try...just get something decent in the 15wpc-35wpc range and you should be fine. Your speakers are pretty efficient so you can really go to town and see what’s out there."
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That sums it up.
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Try a THE FISHER, SCOTT or LAFAYETTE tube amp from 1960-1970.
These are point-to-point soldered and whatever breaks can be replaced.
That can not be said for amps with circuit boards.
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The jump from Solid State to well-done vintage tube amps is VERY EXTREME quality gain. The improvements from one good to a very expensive tube amp less so.
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Vintage tube amps have very good MM phono. So if you are not into Moving Coil, no phono-preamp is needed. (I use a Step-Up-Transformer) .
I was very much into amp shopping and cables - until I found tube gear and now I do not care any more for "better sound".
My system sounds so mellow, musical, transparent and tonally "just right" - with cheap copper cables - that I feel I have my priorities right.
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Stop messing around with expensive cables - start tube rolling with (more or less) expensive tubes.

I can't believe nobody has yet pointed you at the VTA website.

Their SP14 preamp is the equal of any $5k preamp you'll find on Audiogon.  You can build it as a kit for $1090, or you can get it fully assembled and tested for $1490.  90% of their buyers get the kit version.  Excellent instructions and soldering for tube gear isn't all that hard to do.  But even fully assembled, it's much less expensive than the my-poo-don't-stink brands you see around.  It has a very Plain Jane look, so if you want it looking much nicer, Don Sachs takes their boards, builds them in a much more attractive form and sells them for about $2500.  You have a lot of choices to get an exceptional tube preamp.

Lastly VTA offers many tweaks to these things in terms of special pots, caps and remote control if you want it.  All very reasonably priced.

VTA also offers the Bob Latino line of power amp designs which are based upon the old Dynaco amps, but significantly upgraded.  Their ST-120 amp is a Mac 275 killer.  Again, all at very reasonable prices.  For your $5k budget, you could build their top line PH16 phone preamp, the SP14 line stage preamp, and a pair of their 120 watt monoblock power amps.

It's good to have choices.

Try a pair of Quicksilver Mono blocks and a Quicksilver preamp, they are great and super good values. 

bilyeauxbrew, I tried the PS Audio GCD and S300 on extended review.
I have to tell you that replacing the GCD with a tube preamp yielded a really great improvement and synergy with the S300 amplifier (which I rate highly).
In my case, I replaced it with a Van Alstine Transcendence 8 preamp and I have no intention of ever replacing it. It's really superb. With the S300 you'll have remarkable amplification.