A sump pump will certainly be strong enough. They're meant to push water 8-12' up minimum. But it's taking up a lot of room in your bucket. Kinda defeating the purpose of your 5gal.
I can see why you chose a 5gal bucket. But in my not so humble opinion, I think you may eventually realize that the real solution to mechanical filtration is to separate it completely from the bio-filter container & put it in it's own package. Then the 6" PVC isn't such a bad idea, expense aside. I hope your idea works though.
If you find you have leaks at the inlet & outlets, consider ordering some PVC bulkhead fittings. They're meant for this kind of think & will make a much better seal. They're not expensive either.
I can see why you chose a 5gal bucket. But in my not so humble opinion, I think you may eventually realize that the real solution to mechanical filtration is to separate it completely from the bio-filter container & put it in it's own package. Then the 6" PVC isn't such a bad idea, expense aside. I hope your idea works though.
If you find you have leaks at the inlet & outlets, consider ordering some PVC bulkhead fittings. They're meant for this kind of think & will make a much better seal. They're not expensive either.