Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A_2^{(2)}$

We give Andrews-Gordon type series for the principal characters of the level 5 and 7 standard modules of the affine Lie algebra $A_2^{(2)}$. We also give conjectural series for some level 2 modules of $A_{13}^{(2)}$.