If a 2.0g sample of water at 5.0celcius absorbs 21.8joules of energy, the temprature of the sample will be raised by

You'd use the temperature change equation. The specific heat of water is always 4.18J/(g °C).
Equation to use: q=mCΔT

21.8=(2.0)(4.18)(Tf-5)
21.8=(8.36)(Tf-5)
21.8/8.36=Tf-5
2.61=Tf-5
2.61+5=Tf
Tf=7.61 °C

Since you want to know how many °C it raises, you wouldn't pay attention to the last 2 steps, however if you need to know the final temp, you want to go to the last step.