How to add page numbering with php?

I made a custom php page for a category, and want to restrict the max limit of posts per page to 5, and have next and prev buttons. Can someone help?

<?php 
/**
* Video Template
*/

get_header(); ?> 

<section id="primary" class="site-content">
<div id="content" role="main">

<?php 
// Check if there are any posts to display
if ( have_posts() ) : ?>

<header class="archive-header">
<h1 class="archive-title">Videos list<?php single_cat_title( '', false ); ?>
</h1>


<?php
// Display optional category description
 if ( category_description() ) : ?>
<div class="archive-meta"><?php echo category_description(); ?></div>
<?php endif; ?>
</header>

<?php

// The Loop
while ( have_posts() ) : the_post(); ?>
<h2><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link 
to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h2>
<div class="entry">
<small><?php the_time('F jS, Y') ?></small>
<?php the_content(); ?>

</div>

<?php endwhile; 

else: ?>
<p>Sorry, no posts matched your criteria.</p>


<?php endif; ?>
</div>
</section>



<?php get_footer(); ?>

Solutions Collecting From Web of "How to add page numbering with php?"

to change the number of ‘posts_per_page’ for one specific category archive page (assuming your are using a different number for all other archives), try working with the ‘pre_get_posts’ action; see https://codex.wordpress.org/Plugin_API/Action_Reference/pre_get_posts

assuming that your category template is for the ‘video’ category, the code to be added into functions.php of your (child) theme, could be, for example:

function video_category_pagesize( $query ) {
    if ( is_admin() || ! $query->is_main_query() )
        return;

    if ( is_category( 'video' ) ) {
        // Display 5 posts per page for the 'video' category archive
        $query->set( 'posts_per_page', 5 );
        return;
    }

}
add_action( 'pre_get_posts', 'video_category_pagesize' );

for the next prev buttons, for example, consider to use https://codex.wordpress.org/Function_Reference/next_posts_link and https://codex.wordpress.org/Function_Reference/previous_posts_link
and review https://codex.wordpress.org/Pagination