Here's what rhymes with distinguishable.

Consider these alternatives

indistinguishable / distinguishable recognizable / advisable identifiable / viable recognisable / unrecognisable distinguishing / extinguishing differentiated / dated delineated / dated correspond / want attested / requested protruded / included deviations / relations protrude / food differentiates / states deviates / states decipherable / indecipherable accentuated / dated emanate / late perceivable / feasible differentiate / state chiasmus / use