To solve this expression, we will first convert all the mixed numbers into improper fractions:

4 4/5 = (54 + 4)/5 = 24/5
2 2/7 = (72 + 2)/7 = 16/7
5 1/4 = (45 + 1)/4 = 21/4
7 11/12 = (127 + 11)/12 = 95/12

Now, the expression becomes:

24/5 + 16/7 x 21/4 - 95/12

Next, we will simplify the multiplication:

(24/5) + (16/7)(21/4) - (95/12)
= 24/5 + (336/28) - 95/12
= 24/5 + 12 - 95/12

Now, we need to find a common denominator to combine the fractions:

Common denominator = 5*12 = 60

= (2412)/(512) + 12(60/60) - (955)/(12*5)
= 288/60 + 720/60 - 475/60

Combine the fractions:

= (288 + 720 - 475) / 60
= 533/60

Therefore, the final answer is 533/60 or as a mixed number, it simplifies to 8 53/60.