Single post page from static home not working

See the change of get_permalink to the_permalink

This might work for you.

<?php
                $args = array( 'numberposts' => 5, 'order'=> 'ASC', 'orderby' => 'date' );
                $postslist = get_posts( $args );
                foreach ($postslist as $post) :  setup_postdata($post); ?> 
                    <div class="single_post">

                        <h3><?php the_date(); ?></h3>

                        <h3>
                            <a href="https://wordpress.stackexchange.com/questions/109174/<?php the_permalink();?>">
                                <?php the_title(); ?>   
                            </a>
                        </h3>
                        <?php the_excerpt(); ?>
                    </div>
            <?php endforeach; ?>