Quote from uberman

1. Does the ninja have to be firghting the same opponent for the additional damage?
E.g. ninja kits crawler for 5 damage, ninja hits same crawler for 6 damage and kills it. Ninja hits a different crawler, does he hit for 5 (back to start) or 7 (continued to stack) damage.

2. Does moving reset the sequence of increase?

E.g. ninja kits crawler for 5 damage, ninja hits same crawler for 6 damage and kills it. Ninja moves to hit a different crawler, does he hit for 5 (back to start) or 7 (continued to stack) damage.

E.g. ninja kits crawler for 5 damage, crawler runs away and ninja follows so ninja hits same crawler, does he hit for 5 (reset by move) or for 6 damage (sequence of stacking continued. The he killed the crawler so moves to hit a different crawler, how much damage will the first hit on the new target do?

Quote from jli

No. Let f(n) represent damage done on the nth strike, let d represent the base damage (initial damage done), and let k represent the damage increase per consecutive hit.
f(n) = {
k(n-1) + d for all 1 <= n <= 5
4k + d for all n > 5
}