Sort multiple cells based on frequency

Hi all, first off a big thank-you to anyone who responds because I cant work this out!

I have a set of numbers in different cells. I want to sort the range based on the frequency of the number pattern in the row re-occuring.

So the below illustrates the challenge with an example, with the first table being the random numbers (the numbers 1,2,3,4,5 represent the rows and A1 – A5 the column header and not the data) and the second table shows the data set sorted based on frequency of occurence of the row of 4 cells. The rules requires that the 4 exact numbers repeat. 1,5,3,4 occurs 3 times, 2,5,1,3 occurs once and 4,5,5,5 occurs once. 

Data before sort      
  A1 A2 A3 A4
1 1 5 3 4
2 2 5 1 3
3 4 5 5 5
4 1 5 3 4
5 1 5 3 4
         
         
Data after sort      
  A1 A2 A3 A4
1 1 5 3 4
2 1 5 3 4
3 1 5 3 4
4 2 5 1 3
5 4 5 5 5

By: Gareth

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