You can predict the sign of the entropy by looking at the change in the number of moles of gas. Gases have higher entropies than liquids which have higher entropies than solids, since entropy is a measure of disorder. In this reaction there are two moles of gas in our reactants and no moles of gas in our products, indicating that delta S will be negative.
As for the enthalpy delta H, you either need to be told whether the reaction is endothermic or exothermic, or given the enthalpies of formation for the products and reactants, which would be included in the back appendix of most chemistry textbooks. So you are missing some information here.
For Cl2(g) and Si(s) you actually don't need to look them up, the enthalpy of formation for any element in it's standard state is zero. I took a second to look up the enthalpy of formation for the liquid product, it is negative, making delta H for this reaction negative.
