get_posts() is for ‘secondary’ loops – ones that exist along-side the main Loop, usually in a side-bar or at the bottom listing ‘related’ posts etc. get_posts() is called from within a template page. So it is the wrong thing to use here.
You’ll want to alter the main query as outlined in: When to use WP_query(), query_posts() and pre_get_posts
add_action('pre_get_posts','wpse50857_alter_query');
function wpse50857_alter_query($query){
//Check other conditionals depending on when you want to alter the loop
if( $query->is_main_query() && is_home() ){
$tax_query = array(array(
'taxonomy' => 'post_tag',
'field' => 'slug',
'terms' => 'my-tag'
));
$query->set('tax_query',$tax_query);
$query->set('posts_per_page',5);
}
}
Note this over-rides any previous tax_query (this doesn’t matter in this context – but if it should you can get the previous tax_query and merge it with the new one…)
Other conditionals available here.
To edit how the posts are display, you’ll need to edit the appropriate template page (home.php?, front-page.php?).
The loop will be something like:
if( have_posts() ):
while( have_posts() ): the_post();
//The loop
?>
<h1 class="entry-title"><a href="https://wordpress.stackexchange.com/questions/50857/<?php the_permalink(); ?>"><?php the_title(); ?></a></h1>
<?php
endwhile;
endif;
and you can edit that the display whatever you like.