Exotic decays and collider signatures of pseudo-Nambu-Goldstone bosons in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>5</m

The nature of the Higgs boson, whether it is elementary or composite, will be investigated through precision measurements at the collider experiments. In composite Higgs scenarios, the Higgs may manifest as a pseudo-Nambu-Goldstone boson (pNGB) arising from a strongly interacting sector. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>5</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo>/</a:mo> <a:mi>S</a:mi> <a:mi>O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>5</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> composite Higgs model features a rich scalar sector, with the decay patterns of the scalars being heavily influenced by the way fermions are embedded in various representations of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>S</g:mi> <g:mi>U</g:mi> <g:mo stretchy="false">(</g:mo> <g:mn>5</g:mn> <g:mo stretchy="false">)</g:mo> </g:math> . We discuss how masses of the pNGB scalars and their couplings depend functionally on the compositeness scale and the parameters of the strong sector. Unique decay modes of the scalars emerge from the model when the mixing among the various pNGB scalars is non-negligible. We present a comprehensive and thorough analysis of the fermiophilic and fermiophobic decay modes of the pNGB scalars. Significant differences are observed in the decay patterns of the two singly charged scalars. Further, the decay of one pNGB to another on shell pNGB when masses exceed about 1 TeV presents a rich phenomenology, leading to distinctive signatures at the colliders. In this context, the future muon collider offers a promising avenue for detecting pNGB scalars with masses larger than 1 TeV, especially in final states involving <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>W</k:mi> <k:mo>/</k:mo> <k:mi>Z</k:mi> </k:math> fatjets.