By a rival newspaper (5)
I believe the answer is:
times
This might be a double definition.
'by' is the first definition.
('times' can mean multiplied by)
'a rival newspaper' is the second definition.
'times' can be an answer for 'newspaper' (The Times is an example). I am not sure about the 'a rival' bit.
Can you help me to learn more?
(Other definitions for times that I've seen before include "''For the ..., they are a'changin'''(Bob Dylan)" , "measures the length of something" , "Thunderer?" , "Square in New York" , "Big Apple's theatre district" .)