At 5 oclock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in$ \left(\dfrac{60}{55} \times 40\right) $min=43$ \dfrac{7}{11} $min.

$\therefore$ Required time = 43$ \dfrac{7}{11} $min. past 5.