What ammo is it? What kind of surplus? How old are they (can you check headstamps)? How damaged are the rounds?
If the rounds are not damaged and it's just surface dirt (which is what it sounds like), I would just wipe them the best I could and not worry about it for training/plinking purposes.
If you are a soldier going into battle, an LEO, or using it for defensive purposes then I would perhaps think about picking up some other ammo.
That being said, I have had only the best of luck with surplus 5.56; South African, Radway Green, IMI, Prvi Partisan, and many other older surplus brands that I am forgetting. Sometimes it's dirty, in which case I just wipe it and go. I still think you should inspect all rounds for serious damage before loading (a good habit even for new ammo).
In fact the only time I can remember I ever had a problem was when I ordered 10K of the surplus Guatemalan 5.56 in 2003 and about half my crates arrived like this:
(Yes that is my actual photo.) It turns out they had been from the bottom of a pallet that had been sitting in water for years. Unless it's that bad, I would not worry about it.
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