Specific heat formula is Q=M*C*ΔT
Q is amount of energy (4786 J)
M is mass (89.0 g)
C is specific heat (unknown, answer will be in J/gºC)
ΔT is the change in temp (89.5-23.0=66.5ºC)
Let's plug it in.
4786=89.0(C)(66.5)
4786=5918.5(C)
/5918.5
C=.8086508406 J/gºC
with sig figs...
C=.809 J/gºC