The verdict

CPU
GMKtec NucBox K11 has 1x the CPU throughput (29,273 vs 28,854 PassMark).
Idle power
GMKtec NucBox K11 idles lower (10W vs 28W) - cheaper to run 24/7.
RAM ceiling
Minisforum N5 takes more RAM (96GB vs 64GB).
Local AI
Minisforum N5 has a PCIe slot for a low-profile GPU - the other needs a DIY build for local LLMs.

Which wins for each job

Job GMKtec NucBox K11 Minisforum N5
Plex / Jellyfin ~5 streams ~5 streams
Frigate NVR add a detector add a detector
Proxmox / VMs 29,273 PassMark win 28,854 PassMark
Firewall / router 2 NICs 2 NICs
Local AI / LLM no slot PCIe GPU slot win

Approximate - capacity estimates from curated specs, the same logic as the recommender. Verify against your exact setup. Prices move; check the retailer.

Full specs

Spec GMKtec NucBox K11 Minisforum N5
Price (list) $649 $510
CPU AMD Ryzen 9 8945HS AMD Ryzen 7 255
Cores / threads 8 8
PassMark 29,273 28,854
iGPU Radeon 780M (RDNA3) Radeon Graphics (RDNA2)
NICs 2 2
NIC model Intel I226-V dual Marvell AQC113 10GbE plus Realtek 5GbE
RAM max (GB) 64 96
M.2 free 1 3
PCIe slot none x16
Idle (W) 10 28
TDP (W) 54 65