I am confused with adiabatic expansions. I have a homework problem wherein 2.75 moles of an ideal gas at 375 K expands adiabatically with an initial pressure of 4.75 bar and a final pressure of 1.00 bar with a C(p,m)=5R/2. I need to calculate the work done by the expansion.

Where do I start (I don't want just the answer, as I could have just copied that from the back of the book)?

Adiabatic means that there was no heat exchange with the environment $\Delta Q=0$. Thus, by the 1st law of thermodynamics, the work done by the gas is equal to the change in internal energy: $A=\Delta U$. Since this is an ideal gan, it's internal energy is function of temperature only. You just need to use the right formula for the internal energy...