Let's see if I can help shed some light....

Your new dryer needs a 30 amp 240 volt circuit as a minimum. A larger capacity circuit would be okay, as long as the wall receptacle matches the plug from the dryer. Usually different amp rated circuits have different NEMA receptacles (link below).

The amperage rating of a circuit is based mainly on the current capacity of the wire used to wire the circuit from the panel to the receptacle. The breaker size is chosen to protect the wire so it doesn't melt if it is overloaded or shorted. At a minimum, #6 wire is needed for a 50 amp circuit.

It sounds from your description that you have a 50 amp 240 volt dryer circuit available in your apartment? Are those hot wires #6 copper? If they're smaller than #6, then the breaker could be incorrectly sized. But we'll assume that the breaker size and wire size is correct.

It sounds like your dryer cord doesn't match the receptacle already on the wall?

Here's a chart that shows the various configurations:
http://nooutage.com/nema_configurations.htm

Does your dryer cord match up to the 5-30R receptacle in the 30 amp section? If so, what configuration is the receptacle on the wall? Maybe you could post a photo or two and that would help identify things....

I think you're on the right track....

Randy