How much energy as heat is removed from the hand when 5.00 grams of Ga initially at 20 degrees C melts? The value of Heat Fusion is 5.576 kJ-mol and the specific heat of Ga is 0.374 J-g-K. Take the final temp to be 29.76 degrees C.

I don't think the question is worded right. if you want just the heat removed by melting Ga all you need is

q = 5grams x heat fusion = ?.

If you want, and I don't know why the specific heat is given if you don't want it, is the heat removed before melting at 29.76 when starting at 20C.
q = mass Ga x specific heat Ga x (Tfinal-Tinitial).
Substitute and solve for q.
Then add the two qs together.
Tf = 29.76
Ti = 20