Going straight, criminal watches for dishonest acts (2,3,4,5)
I believe the answer is:
as the crow flies
'going straight' is the definition.
'as the crow flies' can be an answer for 'straight' (I've seen this before). I am not certain of the 'going' bit.
'criminal watches for dishonest acts' is the wordplay.
'criminal' is an anagram indicator.
'dishonest acts' becomes 'lies' (I can't justify this - if you can you should give a lot more credence to this answer).
'watches'+'for'='watchesfor'
'watchesfor' anagrammed gives 'asthecrowf'.
'asthecrowf'+'lies'='AS THE CROW FLIES'
Can you help me to learn more?
(Other definitions for as the crow flies that I've seen before include "By direct route" , "How rook moves" , "taking shortest route" , "move in a straight line" , "without deviating" .)