Survive desert, a place of desperation (4-5)
I believe the answer is:
last-ditch
'a place of desperation' is the definition.
I can't judge whether this definition defines the answer.
'survive desert' is the wordplay.
'survive' becomes 'last' (synonyms).
'desert' becomes 'ditch' (ditching is a kind of deserting).
'last'+'ditch'='LAST-DITCH'
Can you help me to learn more?
(Other definitions for last-ditch that I've seen before include "Final recourse" , "Of an attempt or stand, final and desperate" , "Stitch lad up in final defence" , "Denoting final attempt (to do something)" , "Eleventh hour" .)