amps = 5.8 kw/.24 = 24 amps. Check the NEC table 310.16 for
cable ampacity. On the surface #10 thhn would do the job but you have not give all the info required to make the decision.
I'm thinking free air vs. direct burial, full rating vs derated for multiple conductors, 60 deg. vs 90 deg. Oh, any high ambient conditions? 100% loading or 80% loading?
Like David said!
Bill
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"Why not the best?"
Jimmy Carter