Pagination for two loops

You have to pass pagination parameters to your queries as well. As it is, you are just pulling 5 posts. By default that is going to be the most recent five. Then another query pulls the next five. The fact that you are trying to paginate two loops makes this trickier than normal. However…

At first at first I thought you were pulling two different post types or categories, but it looks like you are just creating two loops of the same type– there is no parameter that would do anything different. You can simplify this to a single query and make pagination easier.

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$my_query = new WP_Query( 
    array(
        'showposts'=>10,
        'paged'    => $paged 
    )
); 

?>
<div id="first-loop-container">
    <?php 
    $i = 0;
    while (5 >= $i) : 
        $my_query->the_post(); ?>
        <h4 title="<?php the_title(); ?>"><?php the_title(); ?></h4>
        <?php the_content(" More...",TRUE,''); 
        $i++; ?>
    <?php endwhile; ?>
</div>
<div id="second-loop-container">
    <?php 
    $i = 0;
    while ($my_query->have_posts()) : 
        $my_query->the_post(); ?>
        <h4 title="<?php the_title(); ?>"><?php the_title(); ?></h4>
        <?php the_content(" More...",TRUE,''); 
        $i++; ?>
    <?php endwhile; ?>
</div><?php

$big = 999999999; // need an unlikely integer

  echo paginate_links( array(
        'base' => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
        'format' => '?paged=%#%',
        'prev_text' => __('« Previous'),
        'next_text' => __('Next »'),
        'current' => max( 1, get_query_var('paged') ),
        'total' => $my_query->max_num_pages
    ) );

You start off grabbing your pagination parameters and saving them to $paged. You use that in your single query. Next you run through the first five posts in the query results, and then the second five. You can do anything you want between the two so long as you don’t clobber or reset $my_query. Then your pagination. You were trying to use the global $wp_query, which was wrong since you are trying to paginate $my_query, so I changed that. I also corrected some markup with your <h4> tag,

See if that works better.