Try reviewing this page on the codex. Using your above template, I would suggest the following:
<?php
if ( is_user_logged_in() ) :
$args = array(
'posts_per_page' => '5',
'author' => get_current_user_id(), // Removes a few lines of code ;)
);
$author_posts = new WP_Query( $args );
?>
<?php /* Author has posts? */ ?>
<?php if( $author_posts->have_posts() ) : ?>
<?php /* Loop through author posts */ ?>
<?php while( $author_posts->have_posts() ) : $author_posts->the_post(); ?>
<a href="https://wordpress.stackexchange.com/questions/74496/<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>"><?php the_title(); ?></a>
<?php endwhile; ?>
<!-- Basic Pagination -->
<div class="navigation"><p><?php posts_nav_link(); ?></p></div>
<!-- Or using Wp Pagenavi (http://wordpress.org/extend/plugins/wp-pagenavi/) -->
<?php if( function_exists( 'wp_pagenavi' ) ) wp_pagenavi( array( 'query' => $author_posts ) );
<?php wp_reset_postdata(); /* Important after a custom query. */ ?>
<?php else : ?>
<p>Sorry you have no posts.</p>
<?php endif; ?>
<?php else : ?>
<p>Not logged in</p>
<?php endif; ?>