Try with a custom WP_Query to rule out any possible code messing up with your main query pagination. Like this:
<?php
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$query = new WP_Query( array( 'post_type' => 'post', 'post_status' => 'publish', 'posts_per_page' => 5, 'paged'=> $paged) );
?>
<?php while($query->have_posts()) : $query->the_post(); ?>
<div class="blogcontent">
<div class="post_img"><a href="https://wordpress.stackexchange.com/questions/364381/<?php the_permalink(); ?>">
<?php $img = wp_get_attachment_url( get_post_thumbnail_id($post->ID) ); ?>
<?php $image_alt = get_post_meta( get_post_thumbnail_id($post->ID), '_wp_attachment_image_alt', true); ?>
<?php if($img) { ?>
<img src="<?php echo $img; ?>" alt="<?php echo $image_alt; ?>">
<?php } ?></a></div>
<div class="post_content">
<?php
$category_detail=get_the_category($post->ID);//
foreach($category_detail as $cd){ ?>
<a href="<?php echo get_home_url(); ?>/category/<?php echo $cd->slug; ?>/"><span class="boldtag"><?php echo $cd->cat_name; ?></span></a>
<?php }
?>
<h1><a href="https://wordpress.stackexchange.com/questions/364381/<?php the_permalink(); ?>"><?php the_title();?></a></h1>
<?php the_excerpt(); ?>
<ul class="author clearfix">
<li>By <em><?php the_author_posts_link(); ?></em> <span>ยท <?php the_time('M d, Y') ?></span></li>
<li><a href="https://wordpress.stackexchange.com/questions/364381/<?php the_permalink(); ?>">MORE...</a></li>
</ul>
</div>
</div>
<?php endwhile; ?>
<div class="paginationsec">
<nav class="navigation pagination show">
<div class="nav-links">
<?php
echo paginate_links( array(
'base' => str_replace( 999999999, '%#%', esc_url( get_pagenum_link( 999999999 ) ) ),
'total' => $query->max_num_pages,
'current' => $paged,
'format' => '?page=%#%',
'show_all' => false,
'type' => 'plain',
'end_size' => 5,
'mid_size' => 1,
'prev_next' => true,
'prev_text' =>__( '<i class="fa fa-angle-double-left"></i> Prev', 'twentyfifteen' ),
'next_text' => __( 'Next <i class="fa fa-angle-double-right"></i>', 'twentyfifteen' ),
'before_page_number' => '<span class="meta-nav screen-reader-text">' . __( '', 'twentyfifteen' ) . ' </span>',
'add_args' => false,
'add_fragment' => '',
) );
?>
</div>
</nav>
</div>