let

a = the age of Ana

b = the age of Beth

c = the age of Cathy

Ana is 5 times old as Beth and 2 2/3 times as old as Cathy

a = 5b

Ana is 2 2/3 = 8/3 times as old as Cathy

a = (8/3)c

5b = (8/3)c divide both sides by 5

b = (8/3)(1/5)c

b = (8/15)c

Beth's age is 8/15 of the Cathy's age.