I have a few ideas.
Hardlight Spear - Something close to what the Promethean Knights use. It could be an orange-ish spear (sort of like the Flood Talon) and would have some sick jabs and killing moves. The assassination would be the spartan shoving it through the enemy's face (or wing/head if it was a watcher or crawler).
I saw some GoW ideas, and here is what I would see.
These would either come as separate weapons or attachments if Halo 5 has those.
AR w/ UNSC mk. 087 Gunsaw - In short words, a Lancer. It would be an assault rifle with a chainsaw perfect for sawing the throats of Covies. It would penetrate shield and be truly awesome.
Battle Rifle or DMR w/ UNSC MKT Bayonet - A Retro Lancer. It would be a precision weapon with a blade, which would increase melee radius and damage.
Covenant Carbine w/ Sangheili Ion Blade - Same idea as the last in Covenant form.
FINALLY,
Shieldbreakers! - Brass knuckles that weren't really brass. It'd be a super strong melee substitute but would take away your secondary.