get all posts ID from a category

The thing to remember about get_posts is that is uses a WP_Query object internally. get_posts source:

<?php
/**
 * Retrieve list of latest posts or posts matching criteria.
 *
 * The defaults are as follows:
 *     'numberposts' - Default is 5. Total number of posts to retrieve.
 *     'offset' - Default is 0. See {@link WP_Query::query()} for more.
 *     'category' - What category to pull the posts from.
 *     'orderby' - Default is 'post_date'. How to order the posts.
 *     'order' - Default is 'DESC'. The order to retrieve the posts.
 *     'include' - See {@link WP_Query::query()} for more.
 *     'exclude' - See {@link WP_Query::query()} for more.
 *     'meta_key' - See {@link WP_Query::query()} for more.
 *     'meta_value' - See {@link WP_Query::query()} for more.
 *     'post_type' - Default is 'post'. Can be 'page', or 'attachment' to name a few.
 *     'post_parent' - The parent of the post or post type.
 *     'post_status' - Default is 'publish'. Post status to retrieve.
 *
 * @since 1.2.0
 * @uses $wpdb
 * @uses WP_Query::query() See for more default arguments and information.
 * @link http://codex.wordpress.org/Template_Tags/get_posts
 *
 * @param array $args Optional. Overrides defaults.
 * @return array List of posts.
 */
function get_posts($args = null) {
    $defaults = array(
        'numberposts' => 5, 'offset' => 0,
        'category' => 0, 'orderby' => 'post_date',
        'order' => 'DESC', 'include' => array(),
        'exclude' => array(), 'meta_key' => '',
        'meta_value' =>'', 'post_type' => 'post',
        'suppress_filters' => true
    );

    $r = wp_parse_args( $args, $defaults );
    if ( empty( $r['post_status'] ) )
        $r['post_status'] = ( 'attachment' == $r['post_type'] ) ? 'inherit' : 'publish';
    if ( ! empty($r['numberposts']) && empty($r['posts_per_page']) )
        $r['posts_per_page'] = $r['numberposts'];
    if ( ! empty($r['category']) )
        $r['cat'] = $r['category'];
    if ( ! empty($r['include']) ) {
        $incposts = wp_parse_id_list( $r['include'] );
        $r['posts_per_page'] = count($incposts);  // only the number of posts included
        $r['post__in'] = $incposts;
    } elseif ( ! empty($r['exclude']) )
        $r['post__not_in'] = wp_parse_id_list( $r['exclude'] );

    $r['ignore_sticky_posts'] = true;
    $r['no_found_rows'] = true;

    $get_posts = new WP_Query;
    return $get_posts->query($r);

}

Which, means, of course, that you can use any of the same arguments that WP_Query accepts. This includes parameters relating to fields.

To get an array of just IDs, you’d need to do something like this:

<?php
$post_ids = get_posts(array(
    'numberposts'   => -1, // get all posts.
    'tax_query'     => array(
        array(
            'taxonomy'  => 'category',
            'field'     => 'id',
            'terms'     => 5,
        ),
    ),
    'fields'        => 'ids', // Only get post IDs
));

Or you can wrap it up in a function for more flexibility.

<?php
function wpse71471_get_post_ids($cat, $taxonomy='category')
{
    return get_posts(array(
        'numberposts'   => -1, // get all posts.
        'tax_query'     => array(
            array(
                'taxonomy'  => $taxonomy,
                'field'     => 'id',
                'terms'     => is_array($cat) ? $cat : array($cat),
            ),
        ),
        'fields'        => 'ids', // only get post IDs.
    ));
}