SIM5320A UART Troubleshooting
Try using coolterm terminal with the following configurations,
Baud-rate 115200(check what is the default baud rate) , In terminal key emulation ,select CR+LF.
In the terminal options,select line mode,now you can type 'AT' in the 
new box that appears below the coolterm window.
Have a check on the following things as well.


Make sure you are pressing the POWER_ON button for at least 4 sec,   and find if the network indication led is blinking.
As per the link you have given, the shield uses an adapter,hence use the rated adapter.


Also check the port you must be connecting to and jumper configurations(if any).