That's very strange! It should be pretty much instant -- certainly no more than 30 seconds. Just to make sure I'm understanding you correctly -- you have your static file mappings set up on the "Web" tab, and all you're doing is changing the CSS/JS in the directories that those mappings point to. But the changes you make can take 5 minutes to come through.
Is that right?
One possibility -- when we serve up a static file, we do caching for you. If a browser sends a message saying "only send me this file if it hasn't changed since June 15, 2017 at 15:08 UTC" and the file hasn't changed since then, our server sends back a message saying "all OK, it hasn't changed". This means that if the clock on your own machine is different to the clock on our servers (no need to worry about timezones, that's all handled automatically) then you might get cached pages back.
A way to check if this is the case -- if you run the "date" command in a bash console, does it match up with the date/time on your machine? (Allowing for timezones -- we're on UTC, you're probably not.)
A way to work around the issue (which might also be a useful way to check) -- if you hold down the shift key while reloading a web page in your browser, that means that the page will be reloaded ignoring all caches, so it might be more reliable if this is a cache problem.