Let $a_1$, $a_2$, $\ldots\,$, $a_{2019}$ be a sequence of real numbers.  For every five indices $i$, $j$, $k$, $\ell$, and $m$ from 1 through 2019, at least two of the numbers $a_i$, $a_j$, $a_k$, $a_\ell$, and $a_m$ have the same absolute value.  What is the greatest possible number of distinct real numbers in the given sequence?
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   If we attempt to have 9 or more distinct real numbers, there would be at least 5 distinct absolute values, which would contradict the given condition. Therefore, the maximum number of distinct real numbers is indeed 8.

The final answer is \(\boxed{8}\).