Given that we need to find the centre and radius of the given circle x² + y² - 4x + 6y = 5.

We know that the standard equation of a circle with centre (a, b) and having radius ‘r’ is given by:

⇒ (x - a)² + (y - b)² = r² - - - - - (1)

Let us convert given circle’s equation into the standard form.

⇒ x² + y² - 4x + 6y = 5

⇒ (x² - 4x + 4) + (y² + 6y + 9) = 5 + 4 + 9

⇒ (x - 2)² + (y + 3)² = 18

⇒ (x - 2)² + (y - ( - 3))² = (3)² - - - (2)

Comparing (2) with (1), we get

⇒ Centre = (2, - 3) and radius = 3

∴The centre and radius of the circle is (2, - 3) and 3.