Answer:
x²/25 - y²/144 = 1
Step-by-step explanation:
In a hyperbola with an equation

The vertices are (a, 0) and (-a, 0) and the asymptotes are y = ±(b/a)x
In this case, the vertices are (5, 0) and (-5, 0), so the value of a is 5.
And the asymptote is y = ±(12/5)x, so the value of b is 12.
Then, replacing a = 5 and b = 12, we get that the equation of the hyperbola is

Therefore, the answer is
x²/25 - y²/144 = 1