Since you're using one the of the default templates the easiest way is:
-Go into the Dashboard --> Pages and Themes
-Choose the Theme that you're using and hit Customize.
-Click on custom CSS
-Add this CSS into the form box

-you're not actually getting rid of it but just not showing it in browsers that support CSS (which are 99% of the browsers out there).
-click Save
-now people will need to use the path to login -http://yoursitename.com/index.php/login...
-or you can use the login block from the marketplace.
- to show the sign in option again, just follow the steps above again but Click Reset and Save when you get to the page that let's you Customize the Theme CSS.

Keep in mind that if you install a custom theme or change themes the sign in link will reappear.

The directions above are actually not the best way to get rid of it however.

The better way is to:
-copy the default theme folder into the Themes folder that exists above the core Concrete5 folder and create a "custom theme".
-Modify the footer.php file in the elements folder to delete the reference to sign in.
-upload and apply and activate the new theme.
-you could also turn off the element in the new theme main.css file using the above code and placing it at the bottom of the file.

I don't recommend doing this in the core concrete5 themes folder because when you upgrade concrete 5 in the future you'll just need to do it all over again.

Concrete 5 upgrades don't effect the folders above the core folder and therefore, your changes will remain.

good luck!

mario

Thanks for the help. I used the first suggestion as it was the easiest to follow.