Country shows about to screen 3rd of May (5)
I believe the answer is:
syria
'country' is the definition.
(I know that Syria is a country)
'shows about to screen 3rd of may' is the wordplay.
'shows' becomes 'airs' (shows on TV).
'about' says the letters should be written in reverse.
'to screen' is an insertion indicator (screen can mean to cover up or shield).
'3rd of may' becomes 'y' (3rd letter of 'may').
'airs' back-to-front is 'sria'.
'sria' going around 'y' is 'SYRIA'.
(Other definitions for syria that I've seen before include "Conflict-torn country" , "Country E. of Lebanon" , "Eastern Mediterranean country" , "Arab republic, independent since 1946" , "Country bordering Israel" .)