  Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic
representation of GL_n(A_F), where F is a totally real field and n is at most
5. We show that for all primes l, the l-adic Galois representations associated
to pi are irreducible, and for all but finitely many primes l, the mod l Galois
representations associated to pi are also irreducible. We also show that the
Lie algebras of the Zariski closures of the l-adic representations are
independent of l.

Number Theory;Representation Theory