Superconducting high entropy alloys (HEAs) are emerging as an exotic class of superconducting materials, providing a unique opportunity to understand the complex interplay of disorder and superconductivity. We report the synthesis and detail bulk and microscopic characterization of a ${\mathrm{Nb}}_{60}{\mathrm{Re}}_{10}{\mathrm{Zr}}_{10}{\mathrm{Hf}}_{10}{\mathrm{Ti}}_{10}$ HEA alloy using transport, magnetization, specific heat, and muon spin rotation/relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements. Bulk superconductivity with transition temperature ${T}_{C}=5.7$ K is confirmed by magnetization, resistivity, and heat capacity measurements. Zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements confirm that the superconducting state preserves time-reversal symmetry, and transverse-field measurements show that the superfluid density is well described by an isotropic $s$-wave model.