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Explanation:

2x² + kx + 5 = 0 has no real roots ⇒ D < 0
⇒ k² – 4 × 2 × 5 < 0
⇒ k² < 40
⇒ -√40 < k < √40
∴ Possible integral values of k are -6, -5, -4, …, 0, …4, 5, 6   …(1)

Also, x² + (k - 5)x + 1 = 0 has two distinct roots ⇒ D > 0
⇒ (k - 5)² – 4 × 1 × 1 > 0
⇒ k² + 25 – 10k – 4 > 0
⇒ k² – 10k + 21 > 0
⇒ (k - 7)(k - 3) > 0
⇒ k ∈ (-∞, 3) ∪ (7, ∞)   …(2)

The integral value of k satisfying both (1) and (2) are
-6, -5, -4, -3, -2, -1, 0, 1, 2 i.e., 9 values.

Hence, option (c).