We feed ours a bit of soaked sugarbeet pellets (I think you always have to soak them for pigs) alongside their pig nuts and a bit of fruit and veg thrown in. Too much sugar beet will make them fat, so while you save on feed costs you might have to pay the butcher extra because they'll be fatter and heavier (but won't actually get any more meat)
They'll not get a lot of protien from natural forraging, think of that as 'enrichment' rather than feeding.
So (short version

) by all means give them sugarbeet and carrots - but in addition to their pig nuts, not instead of

If they're 5 months old, I'd aim for a daily ration per pig of around 3lbs of pig nuts, 1-2 lb of soaked sugar beet and about 4lbs of carrots, split into two meals. Just keep an eye on them (or measure them regularly) to make sure they're growing and not getting too fat and adjust as needed.
HTH
Karen