To solve this problem, we will first subtract the second fraction from the first fraction:

8 5/27 - 2 25/27 = (8 - 2) + (5/27 - 25/27)

= 6 + (-20/27)

Now, we can simplify the fraction:

= 6 - 20/27

To combine the whole number and fraction, we need to convert the whole number to a fraction with the same denominator as the fraction:

6 = 6*27/27 = 162/27

Now, we can subtract the fractions:

162/27 - 20/27 = 142/27

Therefore,

8 5/27 - 2 25/27 = 6 - 20/27 = 162/27 - 20/27 = 142/27 = 1 25/27