Yep. There was an assumption 20 years ago when common switches were 100Mbps and running cat5e that you’d have to upgrade cable to get the next speed tier, 1Gbps.
It propagated wildly, but was always incorrect. Cat5e was very much capable of gigabit Ethernet by design.
It was only beyond gig that you’d need cat6, and even then at short lengths 2.5/5/10Gbe has a good chance of working on cat5e anyway (but don’t do it).