Doubt you'll find anything new much better than your DE-5000 in that price range, maybe look used.
We acquired a Tonghui TH2830 a few years ago for ~$850, this is an excellent lab grade bench LCR meter, superb build quality with meticulous attention to detail and a host of features. This and the higher frequency (and much more expensive) Hioki IM3536 are our Lab Grade Bench LCR meters.
If you can somehow swing for the TH2830 you won't be disappointed, and we've developed some routines for sweeping and plotting for this LCR as well as the ability to do external DC Bias measurements and so on. If you search for this meter, LCR fixtures and "mawyatt" you'll find what we've done. Forgot to mention ours has 5 digit frequency resolution, so you can set measurement frequency to 100.01Hz, 1.0001KHz, or 99.999KHz for example, and it's correct!
There' something about measuring a reference 4.7pF COG 0603 cap at 4.6718pf 10/28/21, then on 4/9/22 at 4.6872pF with an added DC bias adapter and the IM3536 at 4.6864pF, then 5/15/22 at 4.6885pF, then 12/23/22 at 4.6844pF that gives one confidence in these Lab Grade Bench LCR meters, call this
addiction quest for precision and not in a controlled environment, just next to my desk in direct path of AC, with WiFi, phones and such
Anyway, good luck with your LCR
addiction quest
Best,