If the both roots of the quadratic equation x² - mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval:

when roots are real and distinct for ax² + bx + c = 0, then
(1) D > 0
(2) 1 < (α + β)/2 < 5 [clearly from diagram]
(3) f(1) > 0
(4) f(5) > 0
(1) D > 0 ⇒ m² - 16 > 0
m² - 16 > 0 ⇒ m ∈ (-∞, -4) ∪ (4, ∞)
1 < -m/2 < 5
2 < -m < 10
-10 < m < -2
1 - m + 4 > 0 and 25 - 5m + 4 > 0
m < 5 and m < 29/5
m ∈ (4, 5)