The heights of six friends are 51 inches, 56 inches, 59 inches, 64 inches, 66 inches, and 68 inches.
We are given that "Katie is the shortest" = 51 inches
We are given that " Joanne is five inches taller than Katie" = 56 inches
We are given that "Riley is five inches shorter than Peter" = only one pair of heights will fit this description,
namely 64" - 59", therefore, Riley = 59"
That analysis leaves three heights, namely 64", 66", and 68"
We are given that "Only one friend is taller than Paul", which means that only the person who is 68" tall is taller than Paul; therefore, Paul = 66"
We are given that "Colleen is taller than Peter"; therefore, Peter is 64", and Colleen is 68"