It is not impossible to have 10 teams sharing 5 venues, and to have the pairs who share play together in the first round.
Here is an example that I found by modifying one of these. There is balance in the five columns, so the games in one column could all be assigned to one referee.
Below the 10 teams are represented by the numbers 0 to 9.
round HA HA HA HA HA
1 89 53 42 17 06
2 07 12 56 83 49
3 61 74 30 95 28
4 52 08 97 46 13
5 34 69 81 20 75
6 15 90 67 48 32
7 73 86 01 29 54
8 62 41 93 50 78
9 04 27 85 36 19