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(",'));
});