With 25 names there are 300 pairings. You can get 220 pairings with 22 groups of 5:
but you're left with 80 pairings you can't put in groups without repeating pairings:
(2,22) (2,23) (2,24) (2,25) (3,22) (3,23) (3,24) (3,25) (4,22) (4,23) (4,24) (4,25) (5,22) (5,23) (5,24) (5,25) (6,22) (6,23) (6,24) (6,25) (7,22) (7,23) (7,24) (7,25) (8,22) (8,23) (8,24) (8,25) (9,22) (9,23) (9,24) (9,25) (10,22) (10,23) (10,24) (10,25) (11,22) (11,23) (11,24) (11,25) (12,22) (12,23) (12,24) (12,25) (13,22) (13,23) (13,24) (13,25) (14,22) (14,23) (14,24) (14,25) (15,22) (15,23) (15,24) (15,25) (16,22) (16,23) (16,24) (16,25) (17,22) (17,23) (17,24) (17,25) (18,22) (18,23) (18,24) (18,25) (19,22) (19,23) (19,24) (19,25) (20,22) (20,23) (20,24) (20,25) (21,22) (21,23) (21,24) (21,25)