I solved it with the help of Bruno Luong and his multisolver found here. The code below can solve any number of dimensions, considering the first two dimensions are of the same size.
M=rand(5,5,2,3,6);
RHS=[0;0;0;0;1];
sx = size(M);
sy = size(RHS);
dx = ndims(M);
MSOL=MultiSolver(reshape(M,sx(1),sx(2),[]),RHS);
MSOL = reshape(MSOL, [sx(2) sy(2) sx(3:dx)]);