The All Five and Threes game is the same as the All Fives Game and Muggins, but with one difference:
A player scores points not only for making a multiple of 5, but also for making a multiple of 3.

Strategy
In addition to the tiles listed in Alll Fives, the following dominoes are valuable because they take one scoring position into another

Odd Primes

G.P. Jellis, author and editor of the late 'games and Puzles Journal, described in Issue 1,
sept/oct 1987 a variation intersting to mathematicians. An elementary knowledge of number theory is required.

The rules remain essentially the same as for "threes and fives", but scores are also counted for multiples of 7, 11, 13, 17 and larger primes.
For a double 6 set this doesn't change very much, but for the larger sets (double 9, double 12 or even double 15) this adds additional complexity.