Lisa,

There is a schedule whereby 25 people can sit in groups of 5 every day for six days, and each two people are together at a table exactly once. I have pasted one below, but since I copied it from elsewhere, the people are numbered 1 through 25. You'll want to use the first 5 days of this schedule.

I don't think it is possible to schedule the tables as you want. Because of properties of the design that arranges the people, on each day, and at each table, there will be one person who has sat at that table before.

Hope this helps anyway.
--Victoria

[ 1 2 3 4 5 | 6 7 8 9 10 | 11 12 13 14 15 | 16 17 18 19 20 | 21 22 23 24 25 ]

[ 1 6 11 16 21 | 2 7 12 17 22 | 3 8 13 18 23 | 4 9 14 19 24 | 5 10 15 20 25 ]

[ 1 8 12 20 24 | 2 6 15 19 23 | 3 9 11 17 25 | 4 10 13 16 22 | 5 7 14 18 21 ]

[ 1 7 13 19 25 | 2 10 11 18 24 | 3 6 14 20 22 | 4 8 15 17 21 | 5 9 12 16 23 ]

[ 1 10 14 17 23 | 2 9 13 20 21 | 3 7 15 16 24 | 4 6 12 18 25 | 5 8 11 19 22 ]

[ 1 9 15 18 22 | 2 8 14 16 25 | 3 10 12 19 21 | 4 7 11 20 23 | 5 6 13 17 24 ]