  We show that an infinite family of odd complex 2-dimensional Galois
representations ramified at 5 having nonsolvable projective image are modular,
thereby verifying Artin's conjecture for a new case of examples. Such a family
contains the original example studied by Buhler. In the process, we prove that
an infinite family of residually modular Galois representations are modular by
studying $\Lambda$-adic Hecke algebras.
