I think 5 rounds are possible, actually more desirable, as then everyone will get exactly 1 two ball match and 4 four balls. Then, in the four ball play, a player can play with all of his or her own team members exactly once, and against all but one of the opposing team members exactly twice. The two ball pairings are then the opposition pairs that never occur in the four ball play. The following schedule should demonstrate the idea:
(A2 A5 v B1 B4) (A1 A4 v B2 B5) (A3 v B3)
(A4 A5 v B2 B3) (A2 A3 v B4 B5) (A1 v B1)
(A1 A2 v B3 B5) (A3 A5 v B1 B2) (A4 v B4)
(A3 A4 v B1 B5) (A1 A5 v B3 B4) (A2 v B2)
(A1 A3 v B2 B4) (A2 A4 v B1 B3) (A5 v B5)
If you are restricted to 4 rounds of play, then I don't see that you can do any better than simply removing one of the rounds above.
Hope that helps.
