Tina randomly selects two distinct numbers from the set $\{ 1, 2, 3, 4, 5 \}$, and Sergio randomly selects a number from the set $\{ 1, 2, ..., 10 \}$. What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina? The answer should be expressed as a fraction in simplest form \frac{k}{m}. Please find the value of k + m.

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