Tries desperately to take the test again (5)
I believe the answer is:
resit
'test again' is the definition.
'resit' can be an answer for 'test' (I have seen 'Second test' mean 'resit' so perhaps 'test' could also mean 'resit'). I'm not certain of the 'again' bit.
'tries desperately to take' is the wordplay.
'tries' anagrams to 'RESIT'.
However, I'm not sure how the anagram is indicated.
'the' is the link.
Can you help me to learn more?
(Other definitions for resit that I've seen before include "tested again" , "second try at test" , "later exam" , "Take examination again" , "take another exam" .)