Custom post type pagination 404 error

I am trying to get pagination working on a custom theme.

I have a post type with custom taxonomies and I have pagination for those custom taxonomies and that works fine.

However on another part of the site I have another custom post type; I am trying to paginate through the posts in this post type. Currently the posts are in a custom taxonomy also in this post type, the custom taxonomy behaves like a category.

The URL structure is http://www.domain.com/latest-news/, however when I go to http://www.domain.com/latest-news/2/ I get a 404 error, this is the problem.

Here is my code (sorry it’s so long):

<?php
                    $numCats = 0;
                    $paged = (get_query_var('page')) ? get_query_var('page') : 1;
                    $posts_per_page = 5;
                    $offset = ($posts_per_page * $paged - $posts_per_page);
                    $taxonomies = array(
                        'latest-cat'
                        );
                    $args = array(
                      'hide_empty' => false,
                      'parent' => 0,
                      'orderby' => 'id',
                      'order' => 'DESC',
                      'paged' => $paged
                      );
                    $terms = get_terms($taxonomies, $args);
                    foreach ($terms as $term) {
                        $args = array(
                        'post_type' => 'latest_news_item',
                        'oserby' => 'id',
                        'order' => 'ASC',
                        'posts_per_page' => -1,
                        'tax_query' => array(
                          array(
                            'taxonomy' => 'latest-cat',
                            'terms' => $term->term_id
                            )
                          )
                        );
                        $wp_query = new WP_Query($args);
                        while ($wp_query->have_posts() ) : $wp_query->the_post();
                        $numCats++;
                        endwhile;
                        $args = array(
                        'post_type' => 'latest_news_item',
                        'parent' => 115,
                        'orderby' => 'id',
                        'order' => 'ASC',
                        'posts_per_page' => $posts_per_page,
                        'offset' => 0,
                        'paged' => $paged
                        );
                        $wp_query = new WP_Query($args);
                    while ($wp_query->have_posts() ) : $wp_query->the_post();
                    ?>
                    <div class="news-events-item">
                        <h3><?php echo get_the_title(); ?></h3>
                        <?php $content = get_the_content(); ?>
                        <p class="summary"><?php echo wp_trim_words($content, '30', '...'); ?><a href="<?php echo get_the_permalink(); ?>" class="read-more">More</a></p>
                    </div>
                    <?php
                    endwhile;
                    } ?>

The $numCats variable is just to count the number of posts so that I can set up the pagination links, and that part works.