so you know that the vertex are (1, 4),(-5, 4) so you find the center(x,y). with midpoint formula.

in your case center is (-2,4) so lets call this distance from center to vertex 'A'.

-5-(-2)=|-3| , 1-(-2)=|3|, A=3

now you can use hyperbola formula to derive standard form.

you know that A=3 and you have foci F at (3, 4),(-7, 4).