Order of Operations

This puzzle is interactive, or otherwise solvable only when logged in with a team.
Solve 4 / 5 clues to proceed.

Anarchy combatants (final North Missouri regiment) attack on several fronts (5)
Honor and (leaders of granny, nephew, uncle) effect happy endings (4)
(Heads or tails?) Gambler’s coin aggravates dormant bug (4)
Leaders of senators, archdukes, (beheaded dictators) dutifully spoke (4)
Tails of goats, sheep, yeti, (retreating evil) rams, or moles (5)