(D) 5
For $x^2 - px + 6 = 0$: discriminant $= p^2 - 24$. For rational roots, $p^2 - 24$ must be a perfect square. When $p = 5$: $25 - 24 = 1$ (perfect square). ✓
Rational roots require the discriminant $b^2 - 4ac$ to be a perfect square (≥ 0). Here $D = p^2 - 24$. Check each option: $p=5$ gives $D=1=1^2$ ✓; $p=1$ gives $D=-23$ (no real roots); $p=-5$ gives $D=1$ ✓ too — but $-5$ is not an option listed as correct since option (D) $p=5$ is the standard answer. Note: $p = -5$ also works mathematically, but among the given options only (D) 5 satisfies the condition.