Clue: Show Conservative support for May's broadcast on the 15th? (4,4,5)
Answer: WEST SIDE STORY
Explanation: Show Conservative support for May's broadcast on the 15th? (4,4,5)
**TORY** ("conservative") "support for" **WEST'S **(indicated by "May's broadcast" = homophone of "Mae's", as in Mae West) + **IDES **(the middle of the month, so "15th"), thus **WEST'S + IDES + TORY