I am using 5.1 as well. What I see is that if I am in a Space, it takes me to the Home Page for that space. If I am at the Dashboard, or something like an Administrative page, it will take me to the Home page for the Site (as defined in the General Configuration).
I can see where to change the logo on both the site level or the space level, but I don't see an option to associate a URL or action with it.
That's weird, no matter where I am it always takes me to Dashboard...
And it's the same behaviour someone described in the last comments here:
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