The verdict

CPU
Minisforum N5 has 1.8x the CPU throughput (28,854 vs 16,372 PassMark).
Idle power
HP Elite Mini 800 G9 idles lower (5W vs 28W) - cheaper to run 24/7.
Networking
Minisforum N5 has more NICs (2 vs 1) - better for a firewall or VLAN trunk.
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 HP Elite Mini 800 G9 Minisforum N5
Plex / Jellyfin ~5 streams ~5 streams
Frigate NVR ~4 cameras win add a detector
Proxmox / VMs 16,372 PassMark 28,854 PassMark win
Firewall / router 1 NICs 2 NICs win
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 HP Elite Mini 800 G9 Minisforum N5
Price (list) $550 $510
CPU Intel Core i5-12500T AMD Ryzen 7 255
Cores / threads 6 8
PassMark 16,372 28,854
iGPU UHD 770 Radeon Graphics (RDNA2)
NICs 1 2
NIC model Intel I219-LM Marvell AQC113 10GbE plus Realtek 5GbE
RAM max (GB) 64 96
M.2 free 1 3
PCIe slot none x16
Idle (W) 5 28
TDP (W) 35 65