I suspect I can't log in to a particular website b/c I need to clear my cache, but where do I do that, and how?

It may vary slightly by browser, but generally it will be in the browser Preferences under Privacy. Usually clearing the cookies for that site will be what you need to clear -- some sites may have multiple cookies under multiple domain names.

Sometimes you can open a new browser window in Private mode for testing, but some websites won't work particularly if they require the use of cookies.

Also try using a different browser since some sites may have compatibility issues with certain browsers. Try Safari, Firefox, or a Chromium based browser such as Vivaldi or Google Chrome.

Are you running any anti-virus apps, cleaning apps, third party security software, or any browser extensions which may be interfering with the normal operation of macOS and your browser?

Are you using any VPNs, or proxies to access the Internet which the site may not allow you to connect?

What year model iMac and what macOS is it running?

to check, see > Identify your iMac model - Apple Support

I’m asking because some websites do not allow older out dated web browsers.

Do you get an error message when you try to log in?

Thanks for confirming the model and macOS version.

What is the website?