Thank you to Milo for pointing me to the pre_get_posts hook. That was exactly what I needed.
Here is my updated code:
Archive page code
<?php
get_header();
get_template_part( 'include/content', 'head' );
?>
<div class="postcontent nobottommargin<?php if( semi_option( 'blog_sidebar' ) == 'left' ) { echo ' col_last'; } ?> clearfix">
<?php
if ( have_posts() ) :
?>
<div id="posts" class="small-posts clearfix">
<?php
while ( have_posts() ) : the_post();
?>
<div id="post-<?php the_ID(); ?>" <?php post_class('entry clearfix'); ?>>
<?php
get_template_part( 'include/blog/casestudies/post', 'standard' );
?>
</div>
<?php
endwhile;
get_template_part( 'include/blog/navigation' );
?></div><?php
else :
get_template_part( 'include/blog/error' );
endif;
?>
</div>
<?php
get_sidebar('casestudies');
get_template_part( 'include/content', 'foot' );
get_footer();
?>
I then added this to functions.php from the codex
function hwl_home_pagesize( $query ) {
if ( is_post_type_archive( 'emp_case-studies' ) ) {
$query->set( 'posts_per_page', 5 );
return;
}
}
add_action( 'pre_get_posts', 'hwl_home_pagesize', 1 );