Answer
$$\eqalign{
& {\text{Vertices }}\left( { - \sqrt 3 ,0} \right){\text{ and }}\left( {\sqrt 3 ,0} \right) \cr
& {\text{Foci }}\left( { - 2\sqrt 2 ,0} \right){\text{ and }}\left( {2\sqrt 2 ,0} \right) \cr
& {\text{Asymptotes: }}y = \sqrt {\frac{5}{3}} x{\text{ and }}y = - \sqrt {\frac{5}{3}} x \cr} $$
Work Step by Step
$$\eqalign{
& \frac{{{x^2}}}{3} - \frac{{{y^2}}}{5} = 1 \cr
& {\text{The equation is in the standard form }}\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1.{\text{ Then,}} \cr
& \frac{{{x^2}}}{3} - \frac{{{y^2}}}{5} = 1,\,\,\,\,\,a = \sqrt 3 ,\,\,\,b = \sqrt 5 \cr
& c = \sqrt {{a^2} + {b^2}} = \sqrt {3 + 5} = 2\sqrt 2 \cr
& \cr
& {\text{With:}} \cr
& {\text{Vertices }}\left( { - a,0} \right){\text{ and }}\left( {a,0} \right) \cr
& {\text{Vertices }}\left( { - \sqrt 3 ,0} \right){\text{ and }}\left( {\sqrt 3 ,0} \right) \cr
& {\text{Foci }}\left( { - c,0} \right){\text{ and }}\left( {c,0} \right) \cr
& {\text{Foci }}\left( { - 2\sqrt 2 ,0} \right){\text{ and }}\left( {2\sqrt 2 ,0} \right) \cr
& {\text{Asymptotes: }}y = \frac{b}{a}x{\text{ and }}y = - \frac{b}{a}x \cr
& {\text{Asymptotes: }}y = \sqrt {\frac{5}{3}} x{\text{ and }}y = - \sqrt {\frac{5}{3}} x \cr
& \cr
& {\text{Graph}} \cr} $$
