For instance, I'm looking for messages that arrived between 5PM and 10PM from a range of dates, February to August.
How can I easily search for them?
The short answer is no. Gmail's search doesn't include any filters for time; only dates. There may be a browser extension out there that will filter Gmail messages by time, but I haven't seen it. I don't know how familiar you are with coding, but you could possibly write your own, for the browser of your choice. You'd need to take a look at how Google formats the time structure for emails, but it can probably be done.