Ministries rhymes with:
registries, industries, industries', industry's, ministry's, pastries, registries, tapestries, asymmetries, chartres, countries, countries', country's, descarpentries, entries, geometries, industries, industries', industry's, ministry's, pastries, petrie's, pleasantries, registries, sentries, tapestries, toiletries
Ministries sounds like:
master's, masters, masters', masterwork, masterworks, mastrich, mastrich's, mcdaris, mckitrick, mckittrick, mcwaters, mcwatters, megastores, meisters, mesothorax, minister's, ministers, ministers', ministry's, minstar's, misters, mistress, mistresses, mixtures, monasteries, monsters, monstrous, moonstruck, mostar's, musketeers, musters, mysteries, mysterious