Question

a 5.00 gram sample of a metal is heated to 80 degrees Celsius and is placed in a 100 gram sample of water. the temperature of the water rises from 20 Celsius to 20.3 Celsius which of these is most likely to be the metal

Answer 1

You didn't list any choices but here is how you work the problem
heat lost by metal + heat gained by water = 0

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat of the metal. Compare specific heats to determine the identify of the metal.