MATRIX DESCRIPTION OF M-THEORY ON T-4 AND T-5

We study the Matrix theory description of M-theory compactified on T-4 and T-5. M-theory on T-4 is described by the six dimensional (2, 0) f ixed point field theory compactified on a five torus, <(T)over tilde ( 5)>. For M-theory on T-5 we suggest the existence of a new theory whic h is compactified on a <(T)over tilde (5)>. Th, IR description of this theory is given by the (2,0) theory with a compactified moduli space. This new theory appears to be a new kind of a non-critical string the ory. Clearly, these two descriptions differ from the ''standard'' Supe r-Yang-Mills on the dual torus prescription. (C) 1997 Published by Els evier Science B.V.