Show posts by a category not working

Try it with this:

<article>
	<?php
	$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
	$temp = $wp_query;
	$wp_query= null;
	$wp_query = new WP_Query();
	$args = array(
		'posts_per_page' => 5,
		'cat'            => 7,
		'paged'          => $paged,
	);
	$wp_query->query( $args );
	while ( $wp_query->have_posts() ) : $wp_query->the_post();
?>
	<div class="post">
		<h2><a href="<?php the_permalink(); ?>" title="Read more"><?php the_title(); ?></a></h2>
		<p><?php echo substr( get_the_excerpt(), 0, 300 ); ?></p>
	</div>
	<?php endwhile; ?>

	<?php if ( $paged > 1 ) { ?>
	<nav id="nav-posts">
	<div><?php next_posts_link( ' Previous' ); ?></div>
	<div><?php previous_posts_link( 'Next' ); ?></div>
	</nav>
	<?php } else { ?>
		<nav id="nav-posts">
		<div><?php next_posts_link( 'Previous ' ); ?></div>
	        </nav>
	<?php } ?>
	<?php wp_reset_postdata(); ?>
	<?php $wp_query = null; $wp_query = $temp; ?>
</article>

keesiemeijer, thanks a lot, that works perfectly.
Anyway, I was checking other posts, and i found this, which helped, although it does not use wp_query.

https://www.ads-software.com/support/topic/display-the-posts-of-one-category-in-a-page-solved?replies=37

<article>
	<?php
		$args = array(
		'cat' => 7,
		'posts_per_page' => 5,
		'paged' => $paged
	);
	query_posts($args);
	while ($wp_query->have_posts()) : $wp_query->the_post();
	?>
	<div class="post">
		<h2><a href="<?php the_permalink(); ?>" title="Read more"><?php the_title(); ?></a></h2>
		<p><?php echo substr(get_the_excerpt(), 0,300); ?></p>
	</div>
	<?php endwhile; ?>
	<?php if ($paged > 1) { ?>
	<nav id="nav-posts">
		<div><?php next_posts_link(' Previous'); ?></div>
		<div><?php previous_posts_link('Next'); ?></div>
	</nav>
	<?php } else { ?>
	<nav id="nav-posts">
		<div><?php next_posts_link('Previous '); ?></div>
	</nav>
	<?php } ?>
	<?php wp_reset_postdata(); ?>
</article>

$wp_query->query( $args ); is essentially the same as query_posts($args);
To clean up after a call to query_posts, make a call to wp_reset_query() instead of wp_reset_postdata();

I’m glad you’ve got it resolved.

thanks for all