What you are looking for is a ND filter (Neutral Density).
They comes both as a fixed value f/stops and as a variable filter.
Which as it says either takes a fixed value of light or a variable amount. I own a variable which after a few test shots can be matched any lighting situation. The fixed amount ND filter, only matches the particular situation where light (shutter + av + iso (+ev)) comes to this level.
I'm googling a few youtubes:
Money saving tips , Beginner DLSR
I was actually looking for a youtube where some scientists walked through the details of ND, and pending how you turned the two layers, light could or could not travel through the barriers.
Polarization (getting close), Bingo, the scientist explaining it.
The way I see it. The problem with fixed stop is, as you found you picture was slightly burned out. I don't know the situation you were in, but I'll speculate you needed 5 stops in you setup. So could have bought a f/+5 stops ND filter. But tomorrow you see a similar shot you want. This lighting is different so, with the setup you lay out, you need a 15 stop ND filter. Bam your f/5 is plain out of luck, because you still need 10 stops and the image becomes blown.