unordered list loop not showing up in sidebar

You want to use post_type instead of just type and put apostrophes around your post type itself.

Instead of this:

$args = array(
    "type" => post,
    "posts_per_page" => 5,
    "category_name" => "Events"
);

I would do this:

$args = array(
    'post_type' => 'post',
    'posts_per_page' => 5,
    'category_name' => 'Events',
);