Tina randomly selects two distinct numbers from the set \(\{ 1, 2, 3, 4, 5 \}\), and Sergio randomly selects a number from the set \(\{ 1, 2, \cdots, 10 \}\). What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina? Express your answer in the form \(\frac{k}{m}\) in simplest form, and find the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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