Well Done Sir!!5 lbs is going to be tough. To get there, you are going to have to make some compromises. Some, personally, that I would not make.
- Lightwieght barrel. Sounds great, but heats up quickly. Detriment to accuracy. Detriment to your hands. If low rounds count and shot strings are your thing, then this could be an option.
- Handguard is somewhere else that you can save some weight, but, you would be going plastic or going with a much shorter rail to save a few ounces while losing a fair amount of functionality. You can try carbon rails, but meh.
- Can go lightweight BCG - but you are giving up long-term durability of the system, and many struggle to function properly out of the gate and without ideal circumstances. Fine if a competition gun and you have a back-up rifle, but otherwise, is it worth it?
- Save some ounces with a very minimalist stock. You can, but they tend to be very uncomfortable to shoot for me. YMMV
Truthfully, I think too many people care too much about what a scale says. The weight of what people consider "lightweight" is also very arbitrary in nature. Spend time getting a quality rifle together and getting it balanced properly. Get a good sling and learn how to use it effectively. Save some weight in your pack and what you put into it. Get better boots that fit properly. A lil more time a a gym could potentially help as well.
In before "ounces equal lbs, lbs equal pain."