I will assume the matrices are positive semidefinite; otherwise, the problem is non-convex and can’t be handled by CVX. Let n be the num,ber of matrices.
declare the matrices as
variable B(5,5,n) semidefinite
To minimize the max eigenvalue of B(:,:,i, the objective is
minimize(lambda_max(B(:,:,i)))
I will leave it to you how this all comes together in oneCVX program, because I have no idea what your overall objective or constraints are.