At what time between 5 o'clock and 6 o'clock in the morning, will the both hands of a clock of a clock be at right angle?

Given that n = 5 and n + 1 = 6
The hands will make right angle at
(5n ± 15) x 12/11 min past 5 .
⇒ (5 x 5 ± 15) x 12/11 min past 5.
⇒ (25 + 15) x 12/11 min past 5 and (25 - 15) x 12/11 min past 5.
⇒ 40 x 12/11 min past 5 and 10 x 12/11 min past 5.
⇒ 4801/11 min past 5 and 120/11 min past 5.
⇒ 43⁷/₁₁ min past 5 and 10¹⁰/₁₁ min past 5.