High-entropy alloys (HEAs) exhibiting superconductivity are of great research interest, as it displays characteristics of both crystalline and amorphous superconductors. In this regard, the particularly interesting case is the recently discovered Re-based α-Mn structure HEAs. These systems are not only the first HEA superconductors based solely on 5d-elements, but they are also isostructural to Re6X (X = Ti, HF, Zr) family of compounds, which famously shows time-reversal symmetry breaking. Here we propose to study the superconducting properties (HfTaWPt) 0.4[Re] 0.6 and (HfNb) 0.1 [MoReRu] 0.9 by a combination of zero-field (ZF) - and transverse-field (TF)-muon measurements and investigate the evidence for an unconventional component of its superconducting order parameter.