Good one @acresverde! The Count Five came out of the San Jose Garage Band scene of the mid-60’s, as did a couple of other One Hit Wonder bands: The Syndicate Of Sound ("Little Girl") and People (a cover of The Zombies "I Love You"). There was also The Chocolate Watchband, who didn’t have a hit on any of their three albums, but were in the Roger Corman movie "Riot On Sunset Strip".
The Left Banke actually had another hit: "Pretty Ballerina". Both it and "Walk Away Renee" were on their debut album, which is in my LP collection.