how to destroy a city in civ 5?

Civilization 5 – Can’t Destroy This City

No, the nuke is the only military unit capable to destroying a city without taking it over and razing it. All other military units will take over the city and give you the option to raze it (With the exception of a capitol). So those are your only two options for destroying cities.

Breaking Civilization 5 With Culture – Civ 5 is a perfectly balanced game with no EXPLOITS