If I had to pick one go-to fill for a clue like 'bravery' in a mainstream American crossword, 'courage' is the first thing that pops into my head. It's the most literal synonym, seven letters, and crossword constructors love it because it's clean and common. If the clue length is (7), 'courage' almost always fits. If crossing letters disagree, then I start eyeballing shorter options.
For a five-letter slot I'd lean toward 'valor' (US) or 'pluck' depending on tone — 'pluck' feels a little more colloquial, 'valor' more formal. British puzzles might prefer 'valour' with a U. Other decent fills you see in grids are 'nerve', 'guts', 'mettle' (six letters), and sometimes 'gallantry' if the pattern allows. So my instinct is to try 'courage' first, then check the crosses; that little routine usually solves it fast and keeps me feeling smug about my weekend puzzle skills.