To solve this arithmetic expression step by step:

Add 5 5/6 and 8 2/9:
5 5/6 + 8 2/9
Convert both numbers to improper fractions:
35/6 + 74/9
Get a common denominator of 18:
$35<em>3+74</em>2$/18
$105+148$/18
253/18
Simplify:
253/18

Divide 253/18 by 25:
253/18 ÷ 25
Convert 25 to a fraction with a denominator of 18:
$253/18$ ÷ $450/18$ Multiply by the reciprocal:
$253/18$ * $18/450$ 253/450

Subtract 3 1/9 from 3:
3 - 3 1/9
Convert both numbers to improper fractions:
27/9 - 28/9
$27-28$/9
-1/9

Add 1.5 to 27/28:
1.5 + 27/28
Convert 1.5 to a fraction:
3/2
Get a common denominator of 28:
$3\ast 14+27$/28
$42+27$/28
69/28

Therefore, the final expression is:
253/450 - 1/9 + 69/28