Convert the angle to degrees:

$\displaystyle\frac{{{5}\pi}}{{4}}=\frac{{{5}\pi}}{{4}}\cdot\frac{{{180}}^{\circ}}{\pi}=\frac{{{{900}}^{\circ}}}{{4}}={{225}}^{\circ}\usepackage{cmbright}\Huge\$

This is in the third quadrant and its reference angle is $\displaystyle{{45}}^{\circ}\usepackage{cmbright}\Huge\$ . It intersects the unit circle at the point $\displaystyle{\left(-\frac{\sqrt{{2}}}{{2}},-\frac{\sqrt{{2}}}{{2}}\right)}\usepackage{cmbright}\Huge\$ . The value of sine is the y-coordinate:

$\displaystyle{\sin{{\left(\frac{{{5}\pi}}{{4}}\right)}}}=-\frac{\sqrt{{2}}}{{2}}\usepackage{cmbright}\Huge\$