You have missed a & before showposts in the query. Also showposts is depracated. Try using posts_per_page instead.
<?php
$gallery = get_cat_id('gallery');
$shirts = get_cat_id('shirts');
$hoodies = get_cat_id('hoodies');
$excluded_cats="-".$gallery.',-'.$shirts.',-'.$hoodies;
$limit = 5;
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
query_posts( 'cat=" . $excluded_cats . "&posts_per_page=" . $limit . "&paged=' . $paged );
$wp_query->is_category = true; $wp_query->is_home = false;
?>