Bespeaks rhymes with:
speakes, speaks, peakes, peakes', peaks, peaks', peeks, speakes, speaks, antiques, beeks, belgique's, boutiques, cheeks, creek's, creeks, critiques, deak's, eakes, freaks, geeks, greeks, leaks, leeks, meeks, peakes, peakes', peaks, peaks', peeks, reeks, seeks, seix, sheeks, sheik's, sheiks, shrieks, sikhs, sneaks, speakes, speaks, squeaks, streaks, techniques, telephoniques, tweaks, weaks, week's, weekes, weeks, weeks', wreaks
Bespeaks sounds like:
backpack, backpacks, backups, bagpipes, bake-offs, bespeak, biceps, bishop's, bishops, bishops', bookshops, boskovich, bukavu's, bukovsky, busboys