The remaining $A_5$ case you are askingof the strong Artin conjecture was recently settled by Khare and Wintenberger, see Corollary 10.2 in their paper Serre's modularity conjecture (I), Invent. Math. 178 (2009), 485-504. I should add that the proof is very complicated and builds on the deep work of many others (I started to make a list here, but then stopped as it would be quite long and probably incomplete).