adding a DAC/Streamer or what

I am thinking of spending under 10K for both items together. Your thoughts?

There are tons of great DACs and streamers. I of course like the brands and models that we've chosen to carry, as well as many others that we don't carry.

In addition to the budget, it would also help to know what kind of sound character you're looking for. We can make a guess based on your choice of KEF Reference 5 and Pass Labs INT-250, but maybe picking gear that also provides a similar sound would be pushing you too far in one direction, and you'd instead prefer adding more neutral gear. ???

What sound qualities are you looking for and are most important to you?

10K is a healthy amount of samolians to heave at this issue.  Still, I recommend being cost effective, in case you want to upgrade.
As indicated earlier I would buy a great DAC and start with a budget streamer, possibly even a PC.  With that budget I would do something much better than the Chord.  So ask yourself what features you want in a DAC.  I use a Bryson DAC3, which besides being a great DAC, as 4 HDMI inputs.  I have many Blu Rays/DVD-A and Blu Rays and the DSD and other high res formats can be sent to the DAC over HDMI (a television can also outputHDMI).  Perhaps this HDMI feature has zero relevance for you, but the Bryson at about 3.5K is still a great DAC.  The Bryston USB inputs are not inferior to their other digital inputs.  Many DACs have an Achilles Heel and that is unacceptable, because many streamers only stream over usb.  I have also owned the Mytek Manhattan, which has no HDMI but retrieves an unbelievable amount of detail.
  Anyway, I would spend 3-5K on a killer DAC, and start slow on the streamer.  A PC optimized with a program such as Audirvana Plus or the Bluesound Node2i.
Another 1-2 K on  a NAS (Synology or perhaps a Melco  N100) if you have a big CD collection to convert to streaming files

What sound qualities am I looking for was an interesting question. I guess my answer is I would like to compliment my component sounds that I already have in my speakers and the amp/preamp. I love to hear the individual components of the music I am listening to and feel that the other equipment I have purchased are able to do so. I like to listen to jazz, classical, and rock. I am not sure that is what you are asking but there you have it. I like the warmer tones and like to be able to hear the bass also.