what dacs are fast, lively, energetic?

@audiocanada, I use a Chord TT2 DAC with a Chord Hugo Mscaler in a system that I put together from isolated wall outlet to my Focal Utopia hp’s and my living room speakers specifically because I enjoy Chord’s speed, musicality, instrument separation, and soundstage. I’ve demoed DACs from Topping to a dCS Rossini Apex stack, mind blown, including Benchmark, Holo May, Hegel, Weiss, and the Mola Mola Tambaqui which I thought sounded really good too. I simply like the TT2 and MScaler’s sound better for the types of music that I listen too. Good luck tracking down what tickles your fancy. 

I agree with those who are wondering about the pairing of “fast” and DAC. I have a Linn Klimax with Dynamik (2018 generation). Musical as hell, lots of air and separation. It is indeed capable of fast, but musical is the attribute that best describes it.
 

It is also insanely expensive new. I got mine on the used market and now will be sending it in for the Organik upgrade. The PS Audio DirectStream (original version) went to a backup system. No comparison, the Linn is night and day better (at 4x the cost). 

Squared 80 has a point and is squared like me. Lots of great DACs you can test drive before you buy.

+1 Chord DAC.

I never thought I would suggest looking at Topping, but here is a good review of the new Topping d90 III discrete - , discrete meaning it is not like their other DAC’s, it is not a R2R it is a single bit DAC.

Sandu, great reviewer, talks about exactly what the OP is asking for: speed and energy (jump to just after 8:00)

D90 III discrete

Could tide you over until you save up for your 5k budget (?)