x^2/25 - y^2/4 = 1 is the correct simplification of the original hyperbola
now according to your transformation
T(5,-2) I will asssume that you mean that
(x,y) ----> (x+5,y-2)
so the original centre of (0,0) would move to (5,-2) and your new equation is
[(x-5)^2]/25 - [(y+2)^2]/4 = 1
Identify the graph of the equation 4x^2-25y^2=100. Then write the equation of the translated graph for T(5,-2) in general form.
Might be another case of half right=all wrong.
I left off that it's a hyperbola
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
x^2/25 - y^2/4 = 1
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