After logging in you need to press the edit button at top left of your webpage to begin editing.

Yes, I know that.

As I said, I am not sent to the admin/edit part of the Concrete5, I am sent to the site itself.

(edit)

And now... for some reason unknown to me... Signing in to edit, brings me to the edit page (dashboard?)...

Maybe you don't have permissions to edit?

I do (or did). I am the only one on the site. Not sure what happened, but it now does let me edit. #shrug

You said it wasn't sending you to "editing my page" which could mean a number of things, but to me meant that you expected signing in to take you into instantly editing your page. Really tough to know what you mean if you don't bother to verbalize, and its always nice to add things like your version of concrete, what you did right before you lost the ability, does your toolbar show, but not the edit buttons, is this a new install, is it a custom theme or one you downloaded through marketplace etc etc.

Honestly not sure. I was just editing content in a normal block. Hit publish my edits, signed out and then stepped away from my computer.

However, now, not sure why, but I am sent to the right page...