You can turn these numbers into improper fractions. 5 1/3 can be changed to 16/3. 3 5/6 can be changed to 23/6. So now your equation is 16/3 - 23/6= ?
To do this we have to have common denominators. Since 3 times 2 can make 6, which is the other denominator then we can multiply the top which is 16 by 2 as well. This is because whatever you do to the top you have to do to the top. 16 times 2 is 32. Now we have 32/6-23/6. The denominator is going to stay the same so you don't have to worry about it. Take the numerators and subtract them.
32-23=?
You should have gotten 9.
So now you have 9 over 6. You can simplify this with a common factor which in this case is 3. 9 divided by 3 is 3. 6 divided by 3 is 2. You now have 3/2. You can simplify this back into a mixed number and that would give 1 1/2. This is because 2, the denominator, goes into 3 once with a remainder of 1. 1 over 2 is 1/2.
Your answer is 1 1/2.