Unless I’m missing something, the probability of getting all red cards is [sub]26[/sub]C[sub]5[/sub]/[sub]52[/sub]C[sub]5[/sub], and of course the same is true for the probability of getting all black cards. The probability of getting one or the other of these cases is thus the sum of these two probabilities (2 * [sub]26[/sub]C[sub]5[/sub]/[sub]52[/sub]C[sub]5[/sub]) minus the probability of getting both simultaneously (zero).