Step 1 :First, convert all the numbers into a common format to compare them. Convert all the numbers into decimal format.
Step 2 :The fraction \(\frac{23}{5}\) can be converted into decimal by dividing 23 by 5.
Step 3 :The square roots can be calculated using a calculator.
Step 4 :After converting all the numbers into decimal format, compare them and order them from least to greatest.
Step 5 :The numbers in decimal format are -4.358898943540674, 4.56, 4.58257569495584, 4.6.
Step 6 :Order these numbers from least to greatest.
Step 7 :\(\boxed{-\sqrt{19}, 4.56, \sqrt{21}, \frac{23}{5}}\) are the numbers in order from least to greatest.