Final answer:
The vertices of the hyperbola with the equation (x-4)²/25 - (y+5)²/4 = 1 are at (-1, -5) and (9, -5) as they lie a distance 'a' = 5 from the center (4, -5) along the transverse axis.
Step-by-step explanation:
To find the coordinates of the vertices of the hyperbola given by the equation (x-4)²/25 - (y+5)²/4 = 1, we first recognize that this is the standard form of a hyperbola centered at (h, k) with a horizontal transverse axis. Here, h = 4 and k = -5. The vertices are located at a distance 'a' from the center along the transverse axis, where a² is the denominator of the x-term, so a = 5 in this case. The vertices are thus (4 ± 5, -5) or (-1, -5) and (9, -5).