How to add a new meta key and assign timestamp to posts

A very simplistic method of achieving this would be as follows;

add_action('template_redirect', 'recently_read');
function recently_read(){

    global $post;

    //only run this function for the posts post_type
    if ( !is_single() ) 
        return;

    //get the current time in the format of: 2013-02-22 11:55:51 
    $timestamp = current_time('mysql'); 

    //add the $timestamp variable to the meta_key for this post
    update_post_meta($post->ID, 'reading_this', $timestamp);


}

Note: The above function goes into your theme functions.php file and is hooked onto the template_redirect action which is fired just before displaying the page to the user. At this point, behind the scenes, our recently_read function will fire and add a time stamp under the key reading_this (name it to your liking). This will occur each time this or any post is viewed. If a time stamp already exists for a given post, it will then update the time stamp accordingly.

Then to retrieve a list of posts with this key you would do the following in your theme files where you want those posts to display;

$recently_read = get_posts( 
    array(
        'posts_per_page'  => 5,       //how many posts we want to show at most
        'meta_key' => 'reading_this', //get posts by our meta key
        'orderby' => 'meta_value',    //order posts by the value stored in the key
        'order' => 'DESC'             //order posts in descending order (newest to oldest)
   )
); 

foreach ($recently_read as $read) {
    echo '<a href="'. get_permalink($read->ID) . '">'. $read->post_title .'</a>';
}

The above could be improved a number of ways but this will definitely get you started.

Note: This is void of any logic that determines if the post was viewed in the last X minutes. For that you can apply your own logic to the meta_key named reading_this and manipulate the data to your liking.