Design a rolling five-minute hit counter

Design an in-memory hit counter that supports: ( 1) recordHit(timestamp) to log an event, and ( 2) getCountLast5Minutes(now) to return the number of events that occurred in the past 300 seconds. Assume timestamps are integer seconds and non-decreasing across calls. Explain how to expire outdated events efficiently without storing every hit individually, detail your data-structure choices and time/space trade-offs, target O( 1) amortized per operation with O( 300) space, and implement the API with unit tests.