This is what I got:

Dylan = 53
Ashley = 77
Kyle = 45
Jacob = 24
Shelby = 31

Lets Put it back in the equation:

1. In thirteen years, Dylan's age will be Sixty-Six less than three times the age of Shelby.

------ 53 + 13 = 66 <---- Equals <-----------
31 + 13 = 44 x 3 = 132 - 66 = 66 <----^

2. The sum of the ages of Jacob and Ashley is one hundred one.

77 + 24 = 101

3. Ashley is Thirty-Two years older then Kyle.

77 - 32 = 45 = Kyle's Age.

4. Jacob is Fifty-Three years younger than Ashley.

24 + 53 = 77 = Ashley's Age.

5. Dylan's age is nine less than two times the age of Shelby.

31 x 2 = 62 - 9 = 53 = Dylan's Age.