offset and max_num_pages in pagination gallery

I rewrote the code galleries and stopped at the pagination. How can I get the maximum number of pages? at the moment I can not define it, and put a test for the number 5.

 (Here "for ($ i = 1; $ i <= 5; $ i ++)" here "if ($ paged <5))."

And how to make that work offset parameter in pagination? Now when I put the parameter offset, pagination will not work correctly. I need to post 16 pictures post_per_page was equal to 4. I have not found a solution for my specific case. Maybe it can be replaced with something? Here is my complete code in funсtions.php

    remove_shortcode("gallery");
add_shortcode("gallery","my_gallery");

function my_gallery($atts){
    $img_id = explode(',', $atts['ids']);
    if(!$img_id[0]) {
        return '<div class="no-img-gallery">No images</div>';
    }

    $paged = get_query_var('paged') ? get_query_var('paged') : 1;
    $pictures = get_posts( array(
        'posts_per_page' => 4,
        'post__in'       => $img_id,
        'paged' => $paged,
        'post_type'      => 'attachment',
    ) );

    $html = '<div class="gallery-my">';
    foreach ($pictures as $item){

        $img_desc = $item->post_content;
        $img_caption = $item->post_excerpt;
        $img_title = $item->post_title;
        $img_thumb = wp_get_attachment_image_src($item->ID);
        $img_full = wp_get_attachment_image_src($item->ID,medium);


        $html .="
        <div class='item-gallery'>
            <a href='{$img_full[0]}'>
                <img src='{$img_thumb[0]}' width='{$img_thumb[1]}' height='{$img_thumb[2]}' alt='{$img_title}'>
            <div class='desc-wrap'>
                    <strong class='title-img'>{$img_title}</strong>
                    <span class='desc-img'>{$img_desc}</span>
                </div>
            </a> 
        </div>";

    }

    $html .= "</div>";
//Pagination
    $html .= "<div class='pagination-gallery'>";
        if ($paged > 1) { 
            $html .="<span class='prev-cust'>
                        <a href='?paged=".($paged-1)."'><</a>
                    </span></div>";
        }
        for($i=1;$i<=5;$i++){
            $html .="<span class='num-pag'>
                <a href='?paged=".$i."'";

            if($paged==$i){
                 $usl='class="selected"';
            }
            else{
                 $usl='';
            }

            $html .=$usl.">".$i."</a></span>";
        }
        if ($paged < 5) { 
            $html .="<span class='prev-cust'>
                        <a href='?paged=".($paged+1)."'>></a>
                    </span></div>";
        }

    $html .= "</div>";                              


    return $html;

}