One department in US state given serious examination (2-5)
I believe the answer is:
in-depth
'serious examination' is the definition.
I don't know anything about this answer so I can't tell whether this works.
'one department in us state' is the wordplay.
'one' becomes 'i' (Roman numeral).
'department' becomes 'dept'.
'in' means one lot of letters goes inside another.
'us state' becomes 'nh' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'dept' put inside 'nh' is 'ndepth'.
'i'+'ndepth'='IN-DEPTH'
'given' acts as a link.
Can you help me to learn more?
(Other definitions for in-depth that I've seen before include "searching" , "Thorough and intensive" , "Comprehensive and thorough" , "Profoundly (studied)" , "Full" .)