5.21 b: Recall a number is divisible by $11$ if the alternating sum of its digit s is divisible by $11$. 

5.23: Recall that a number is divisible by $9$ if the sum of its digits is a multiple of $9$.

5.27: Try finding the prime factorization of $6975$ first. Then use this to write $6975$ as the product ot two $2$-digit numbers. 

5.28: Note all possible sums of two of those numbers is greater than $2$, so all of the sums must be odd prime numbers. Use this to try to pair the numbers so you get distinct prime numbers for each pair. 

5.30: Start by looking at the hundreds digit. It must be true that $A=B$ (if there was no carryover from the previous column) or $B = A+1$ (if there was carryover).  Use this to find clues for what are the possible values of $D$ (remember, all digits are distinct).