Wohlfahrt's Theorem for the Hecke group G_5
  Let K be a subgroup of the inhomogeneous Hecke group G_5 of finite index. Suppose that the geometric level of K is r. Then K is congruence if and only if K contains the principal congruence subgroup of level 2r. 
Cheng Lien Lang and Mong Lung Lang
math.GR