Almost certainly not. The usual challenges here are:
1. The codec is computationally expensive (at least by embedded-device standards). Often this is handled by a dedicated ASIC.
2. The waveform needed for DMR (TDMA 4-FSK) or D-STAR (narrowband GMSK) isn't something this radio's hardware is built to generate.
The RF chip in the UV-K5 is a BK4819, which does have some limited F2D+F1W FSK data capability. Anecdotally it sounds like it's limited to 2-FSK though. You might be able to get APRS text messaging / AX.25 packet radio working.
I'm still waiting for somebody to build a truly hackable SDR-based HT that can be programmed with custom waveforms.
I use this custom version of the egzumer firmware https://github.com/kamilsss655/uv-k5-firmware-custom but I don't believe it makes any changes to APRS functionality compared to the repo it's forked from. I believe I also came across a repo with a dedicated APRS firmware being worked on but can't find it at this time.