Filter categories of posts with checkboxes

I was able to solve this by using Ajax.
First I’ve changed my query args:

$args = array(
  'post_type' => 'html5-blank',
  'posts_per_page' => 5,
  'paged' => $paged,
  'category_name' => get_query_var('category_name')
);

Then I made template where my content would change by injecting it with Ajax like this:

var $vbPosts = $('#vb-posts');
var videoCats  = {
    'ux-web-tactics': true,
    'marketing-tactic': true,
    'other-tactics': true,
};

$('#video-checkboxes').on('change', 'input:checkbox', function() {
    var cat = $(this).data('category'); // ux-web-tactics
    videoCats[cat] = this.checked;
    var lookupCategories = [];
    for (key in videoCats) {
        if (videoCats[key] === true) {
            lookupCategories.push(key);
        }
    }

    // This doesnt allow for checkboxes to be turned off
    if (lookupCategories.length === 0) {
        this.checked = true;
        return;
    }
    $vbPosts.load('video-checkboxes/?category_name=" + lookupCategories.join(",'));
});