Questions about replacing cassette

I have a 1997 Cannondale H300. It's a commuter/hybrid kind of thing. It's been jumping out of gear when the fifth cog is engaged, and today I noticed a tooth is missing! So I looked online, and new cassettes (7-speed) are about US$20 or so. The problem is, I don't know which one is compatible with it. I don't have the tools to remove the existing cassette now (I was going to order them with the new cassette), so I'm worried I won't get the right thing.

I was thinking this cassette:

https://www.performancebike.com/microshift-h072-cassette-silver-7-speed-shimano-hg-1228t-cs-h072-12-28t/p1234881?v=750623

Will it work?