Enthalpy and Entropy Changes

$Cl_2(g) \rightarrow 2Cl(g)$ is endothermic (energy is needed to break the bond), so the reverse reaction $2Cl(g) \rightarrow Cl_2(g)$ is exothermic: $\Delta_rH < 0$. Two gaseous atoms combine to form one gaseous molecule, so randomness decreases: $\Delta_rS < 0$.

$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$
The dissociation of $PCl_5$ involves the breaking of two P-Cl bonds, which needs energy, so the reaction is endothermic.
$\Delta H = \Delta E + \Delta n_g RT$, where $\Delta n_g$ = change in the number of moles of gaseous products and reactants.
Here $\Delta n_g = 2 - 1 = +1$, i.e. positive, so $\Delta H$ = +ve.
$\Delta S = S_{products} - S_{reactants}$
One mole of gas gives two moles of gas, so the randomness increases and $\Delta S$ = +ve.
Hence $\Delta H \gt 0$ and $\Delta S \gt 0$.