Force update from unsigned repository

Solution 1:

You can set options in your sources.list (located at /etc/apt/sources.list):

deb [trusted=yes] http://www.deb-multimedia.org jessie main

The trusted option is what turns off the GPG check. See man 5 sources.list for details.

You can either edit the file within the terminal with vim ( or whatever you prefer) or any non-terminal editor like gedit.

Solution 2:

You can bypass some important safeguards by using the following option:

--allow-unauthenticated

From the man pages for apt-get:

--allow-unauthenticated
    Ignore if packages can't be authenticated and don't prompt about
    it. This can be useful while working with local repositories, but
    is a huge security risk if data authenticity isn't ensured in
    another way by the user itself. The usage of the Trusted option for
    sources.list(5) entries should usually be preferred over this
    global override. Configuration Item:
    APT::Get::AllowUnauthenticated.

But be a little cautious about using this option more widely, the safeguards are in place to protect your computer not limit your freedom...

Solution 3:

Another generic solution would be

sudo apt-key adv --keyserver pgp.mit.edu --recv-keys 5C808C2B65558117

Note: I didn't test the solution with this repository but I did it with Skype repository and it worked just fine.

Another solution specific to your case is to install the keys

wget http://www.deb-multimedia.org/pool/main/d/deb-multimedia-keyring/deb-multimedia-keyring_2012.05.05_all.deb -O deb-multimedia-keyring.deb
sudo dpkg -i multimedia-keyring_all.deb

As described in the full walk through Here