Back Rex, for example, in African country (5)
I believe the answer is:
niger
'african country' is the definition.
(country in Africa)
'back rex for example in' is the wordplay.
'back' says the letters should be written in reverse.
'rex' becomes 'R' (abbreviation e.g. GR=George Rex, King George).
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'r'+'eg'+'in'='regin'
'regin' in reverse letter order is 'NIGER'.
(Other definitions for niger that I've seen before include "West African republic" , "African country dominated by the Sahara, until 1969 a French colony" , "River, Africa's largest delta" , "Landlocked W African republic" , "The black" .)