Five-point functions and the permutation group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:math>

Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo stretchy="false">→</a:mo><a:mn>3</a:mn></a:math> scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider the permutation group <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi>S</d:mi><d:mn>5</d:mn></d:msub></d:math> to facilitate the description of such objects. We work out the multiplets transforming under irreducible representations of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>S</f:mi><f:mn>5</f:mn></f:msub></f:math> and provide compact formulas allowing one to cast the permutations of an object <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>f</h:mi><h:mn>12345</h:mn></h:msub></h:math> into combinations with definite permutation symmetry. We also give the explicit expressions for the irreducible multiplet products. We consider several practical applications as examples: We arrange the four-momenta and Lorentz invariants of a five-point function into the multiplet structure, we work out the color tensors of the five-gluon vertex in the multiplet notation, and we discuss applications for five-body wave functions like those of pentaquarks.