Many thanks for these Jolan.
Great fun as always. Here are my attempts-
1. Violent old hand burned to a turn (5-3-7)- Blood and thunder? (anagram of “old hand burned to” – meaning violent)
2. Narrow cap covering a diminutive person (7) Bigoted? (Cap(ital) – Big O covering Ted (diminutive) – meaning narrow)
3. Nebraskan retribution for Lincoln’s assassin? (7,10)- Capital punishment? (The capital of Nebraska is Lincoln)
4. Listen to disheartened tenors encourage working for a theatre performer (5,7) Heart surgeon? (Hear – (listen to) + ts (disheartened tenors) + urge (encourage) + on (working) – heart surgeon, a theatre performer)
5. Bug found in part of the roof and sink (9) Eavesdrop (eaves- part of roof and drop is to sink- eavesdrop is to bug)