Let's simplify the given expression step by step:

\((25)^{-\frac{1}{2}} \times (27)^{\frac{1}{3}} + (121)^{-\frac{1}{2}} \times (625)^{-\frac{1}{4}}\)

First, evaluate the individual terms:

\((25)^{-\frac{1}{2}} = \frac{1}{\sqrt{25}} = \frac{1}{5}\)

\((27)^{\frac{1}{3}} = \sqrt[3]{27} = 3\)

\((121)^{-\frac{1}{2}} = \frac{1}{\sqrt{121}} = \frac{1}{11}\)

\((625)^{-\frac{1}{4}} = \frac{1}{\sqrt[4]{625}} = \frac{1}{5}\)

Now, substitute these values back into the expression:

\(\frac{1}{5} \times 3 + \frac{1}{11} \times \frac{1}{5}\)

Simplify each term:

\(\frac{3}{5} + \frac{1}{55}\)

To add these fractions, they need a common denominator. The common denominator of 5 and 55 is 55:

\(\frac{3 \cdot 11}{5 \cdot 11} + \frac{1}{55}\)

\(\frac{33}{55} + \frac{1}{55}\)

Combine the fractions:

\(\frac{33 + 1}{55}\)

\(\frac{34}{55}\)

Therefore, the simplified expression is \(\frac{34}{55}\).