Answer: Option C
Let the length of sides of the two triangles be a1 and a2 respectively and their altitudes be h1 and h2 respectively.
Then,
$$\eqalign{
& \Leftrightarrow \frac{{\frac{{\sqrt 3 }}{4}a_1^2}}{{\frac{{\sqrt 3 }}{4}a_2^2}} = \frac{{25}}{{36}} \cr
& \Rightarrow {\left( {\frac{{{a_1}}}{{{a_2}}}} \right)^2} = {\left( {\frac{5}{6}} \right)^2} \cr
& \Rightarrow \frac{{{a_1}}}{{{a_2}}} = \frac{5}{6} \cr} $$
And
$$\eqalign{
& \Leftrightarrow \frac{{\frac{1}{2} \times {a_1} \times {h_1}}}{{\frac{1}{2} \times {a_2} \times {h_2}}} = \frac{{25}}{{36}} \cr
& \Rightarrow \frac{5}{6} \times \frac{{{h_1}}}{{{h_2}}} = \frac{{25}}{{36}} \cr
& \Rightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{{25}}{{36}} \times \frac{6}{5} \cr
& \Rightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{5}{6} \cr} $$