How do I pull post from standard post format?

The terms parameter will only accept custom post types and, like you mentioned, post-format-standard is not one.

Try instead to use the ‘NOT IN’ operator to test against the custom posts you don’t want to display (all in this case):

$query = array(
  'showposts' => 5,
  'post_type' => 'post',
  'tax_query' => array(
    'relation' => 'OR', // You likely don't need this
    array(
      'taxonomy' => 'post_format',
      'field'    => 'slug',
      'terms'    => array( 'post-format-video', 'post-format-image', 'post-format-link', 'post-format-aside', 'post-format-quote', 'post-format-chat', 'post-format-video', 'post-format-chat', 'post-format-audio' ), 
      'operator' => 'NOT IN'
    ),
  ),
);

The thinking here is that it won’t display anything but standard posts.

Reference Taxonomy_Parameters

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