jmc

Using the properties of modular arithmetic, $2011\cdot 2012\cdot 2013\cdot 2014\equiv 1\cdot 2\cdot 3\cdot 4$ modulo 5. Continuing, $1\cdot 2\cdot 3\cdot 4\equiv 4$ modulo 5, so $2011\cdot 2012\cdot 2013\cdot 2014\equiv \boxed{4}$ modulo 5.