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I want to connect to SIM5320E module with an ARM CM3 microcontroller and transfer large amount of data like video. How can I do that?
You use the term "CM3". But Cortex-M3 is just the core part of a processor architecture. If you switch from generic Cortex-M3 to specific processors, you should be able to compare the datasheets and see what peripherial support that processor has that happens to match the interfaces of your camera.
Then you can start trying to figure out if you see suitable software written - or if the camera happens to have the suitable documentation so you will be able to write the code yourself.