We know that 60" = 1`

Now, 30" = 30/60 = 1/2 = 0.5`

Now, 37` 60" = 37 + 0.5 = 37.5`

Again 60` = 1^° 

=> 1` = (1/60)^°

So, 30.5` = 37.5/60 = 0.625^°

Now, Now, 5^° 30` 30" = 5^° +  0.625^° = 5.625^°

Again 180^° = π radian

So, 1^° = π/180^°  radian

=> 5.625^° = (π * 5.625^° )/180^°  radian

                 = 5.625^° /180^° π radian

                 = 0.03125 π radian

So, 5^° 30` 30" = 0.03125 π radian