Customize the previous_post_link output

I would just filter previous_post_link and next_post_link. This way, your template stays clean, and you move the extra logic to the functions.php.

Example, not tested:

add_filter( 'previous_post_link', 'filter_single_post_pagination', 10, 4 );
add_filter( 'next_post_link',     'filter_single_post_pagination', 10, 4 );
function filter_single_post_pagination( $output, $format, $link, $post )
{
    $title = get_the_title( $post );
    $url   = get_permalink( $post->ID );
    $text="Read previous";
    $class="prev-post";
    $rel="prev";

    if ( 'next_post_link' === current_filter() )
    {
        $text="Read next";
        $class="next-post";
        $rel="next";
    }
    return "<div class="$class">
            <div class="title1">
                <h5><a href="https://wordpress.stackexchange.com/questions/118697/$url" rel="$rel">$text</a></h5>
            </div>
            <div class="title2">
                <h5><a href="https://wordpress.stackexchange.com/questions/118697/$url" rel="$rel">$title</a></h5>
            </div>
        </div>";
}