well i will tell you this... you haven't picked the easiest cory to spawn. schwartzi has rarely been spawned in the aquarium.
but in general a 5 gallon will work if you are just spawning a pair or trio of smaller corydoras. I would say a ten gallon tank would be better, but in a pinch they may spawn in there. i would add more then just an airstone to the tank. Possible a sponge filter as you most likely would some sort fo filtration within the tank itself as you would hate an amonia spike or something else to happen and kill your fish.
and if you think it is as easy as throwing them in the tank and getting them to spawn right away you are sadly mistaken. some of my corys it has taken more then days to get them to spawn... more like years. it took my green lasers almost 3 years to produce their first spawn.
if you haven't spawned a cory eyt, i would suggest you try something a little easier to spawn.. such as aeneus, paleatus, panda, pygmaeus or even habrosus. all those corys easily spawn within the aquarium with little effort, unlike the shwartzi.