First: write a balanced chemical equation so you can see the mole ratios of reactants and products.
2 HNO3 + CaCO3 --> 2 Ca(NO3)2 + HOH + CO2
Calculate the moles of each reactant to determine if one is a limiting reactant.
moles of CaCO3 = 5g/molar mass of CaCO3
moles of HNO3 = 5 g/molar mass of HNO3
From your results in step 2, you will see that HNO3 is the limiting reactant.
Based on the information from step 3, and the balanced chemical equation in step 1, you know that for every 2 moles of HNO3 you will produce 1 mole of CO2, so find number of moles of CO2 produced.
You know that at STP, 1 mole of CO2 has a volume of 22.4 L. Since you know the moles of CO2 from step 4, calculate the volume of gas produced.
Using Charles's Law, calculate the volume of the gas at SLC, using the volume from step 5, and knowing that the temperature is increasing from 273.1 to 298.1 K.