If you’re asking to change the number of posts from 10 to something else, you can do one of the following
1) Submit the search query as
?s=key&order=ASC&posts_per_page=5
You can achieve this by adding hidden fields to the form. Just change the number to whatever you want
2) Go to Settings > Reading, change the setting there. This will change the setting for all the pages though
3) Add this to your theme’s functions.php or in a plugin
add_filter('pre_get_posts', 'change_posts_on_search');
function change_posts_on_search($query) {
if($query->is_main_query() && $query->is_search())
$query->set('posts_per_page', 5); // change the number here
}
UPDATE IN RESPONSE TO COMMENT
<form action="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>" method="get">
<input type="text" name="s" />
<select name="posts_per_page">
<option>5</option>
<option>10</option>
<option>15</option>
<option>20</option>
</select>
<input type="submit" />
</form>
This form does that work. Basically it’s same as the first option above. But except for the hidden field, it shows the field to the user allowing for changes.