Classifying (almost)-Belyi maps with Five Exceptional Points
  We classify all rational functions whose branching pattern above {0, 1, infinity} satisfy a certain regularity condition with precisely d=5 exceptions. This work is motivated by solving second order linear differential equations, with d=5 true singularities, in terms of hypergeometric functions. A similar problem was solved for d=4 by Vidunas and Filipuk. 
Mark van Hoeij and Vijay Jung Kunwar
math.CO