Function to limit the number of posts in taxonomy.php

Use the pre_get_posts hook to check is you are in a taxonomy term archive and change the number of posts ex:

add_action('pre_get_posts', 'change_tax_num_of_posts' );
function change_tax_num_of_posts( $wp_query ) {  
    if( is_tax() && is_main_query()) {
        $wp_query->set('posts_per_page', 5);
    }
}