I'd like to know if there's any possibility to create a private landing page with an expiration when it is shared to someone, like after 5 days it's turn unavailable.
If not, is there any other solution available on the web?
No, this is not available. But you can set it to noindex to keep it more private.
If you want PURLs, yes this is done, but there's no expiration unless you disable the page.
As Josh said, this is not available in Marketo at this time. However, I've just started working with Uberflip and I believe they let you add content that expires after on a certain date. Not sure if you're okay with looking into a third party, but this way, you'd potentially be able to create landing pages that are only functional for a certain period of time. Again, I haven't toyed around with it yet since I'm still in the process of implementation.