How to delete that row from the matrix which the summation of elements more than 5?

I have matrix :

C =[

     1     0     0     0     0     6
     1     0     0     0     5     6
     1     0     0     4     0     6
     1     0     0     4     5     6
     1     0     3     0     0     6
     1     0     3     0     5     6
     1     0     3     4     0     6
     1     0     3     4     5     6
     1     2     0     0     0     6
     1     2     0     0     5     6
     1     2     0     4     0     6
     1     2     0     4     5     6
     1     2     3     0     0     6
     1     2     3     0     5     6
     1     2     3     4     0     6
     1     2     3     4     5     6];

I need to remove that row, where the number of elements more than 5.

For example the last row of matrix c has 6 elements, so the code should remove the last row from matrix C.

I could write the code, but it is just for one row.

I need to make it suitable for all rows. I have tried, but I couldn't.

Could anyone help me?

My code:

C =[

     1     0     0     0     0     6
     1     0     0     0     5     6
     1     0     0     4     0     6
     1     0     0     4     5     6
     1     0     3     0     0     6
     1     0     3     0     5     6
     1     0     3     4     0     6
     1     0     3     4     5     6
     1     2     0     0     0     6
     1     2     0     0     5     6
     1     2     0     4     0     6
     1     2     0     4     5     6
     1     2     3     0     0     6
     1     2     3     0     5     6
     1     2     3     4     0     6
     1     2     3     4     5     6];
 C~=0,2;
E=size(C,2); 
if sum(C(16,1:E))>5 %<-------this just checking row-16
C(16,:)=[];<---------------and removing row 16
end

Here, in my code I wrote the number of single row manually, but actually right code should find automatically all rows.

Answer 1

[the cyclist]

removeIdx = sum(C>0,2)>5;
C(removeIdx,:) = [];

[Beibit Sautbek]

Your code gave me empty matrix

[the cyclist]

Sorry, I misread your question. I thought you wanted the sum of elements to be less than or equal to 5.

Now I see you want the count of non-zero element to be less than or equal to 5. I have edited my code accordingly. Please try again.

[Beibit Sautbek]

Thank you very much! It works, and I am so happy!