I've built several U/L rifles, it's difficult to get under 5lbs when building a magnum bolt face cartridge, but not impossible, my 280AI is 5lbs 2.4oz on its own, Defiance Anti Action, Alloy Bottom Metal, 23 inch Benchmark #1 contour fluted 1-9 twist barrel, Wildcat Ultra Light CF stock with palm swell and high comb added, if you add a Leupold VX3i 4.5-14x40 ZL-CDS and Talley's it's an extra pound.
You can use a 3.5-10x40 ZL-CDS and save 2oz
My 280AI
And ultralight rifle do shoot even with pencil thin barrels, 100 yard group
292 yard group
Titanium action is an option to save a cpl ounces but not my fav way to go, you could lighten a Rem model seven SAUM/WSM action as another option, if building a non magnum SA cartridge Kimber Mountain Ascent or Montana action is a no brainer but the 8400 action they use for Mag Bolt face WSM cartridges is to heavy to get to your desired weight goals.
I'm going to build a 6.5 PRC on a Defiance Anti Action, Defiance Bottom Metal, Wildcat CF stock, 22 inch Hells Canyon Lite Hunter CF barrel, Alloy Brake, should be around 81-82 ounces so 5lbs 2oz