Edit in JSFiddle

      var x = 0;
      if (window.location.search.indexOf('tumblrpage=') > -1) {
          var url = $(location).attr('href');
          url = url.split('=');
          x = url[1] * 5 - 5;
          currentpage = url[1];
      } else {
          currentpage = 1;
      }

      repeatAjax();

      function repeatAjax() {
          $.ajax({
              url: '<?php echo get_bloginfo("stylesheet_directory"); ?>/tumblr/api.php',
              type: 'post',
              dataType: 'json',
              data: {
                  'tag': '<?php echo $liveblog_tag; ?>',
                  'offset': x
              },

              success: function (posts) {
                  var postings = posts.response.posts;
                  console.log(postings);
                  var text = '';
                  for (var i in postings) {
                      var p = postings[i];
                      text += '<li>';
                      var taglength = p.tags.length;
                      var author = ''
                      var authorfound = 0;
                      var title = '';
                      var social_title = '';
                      var social_handle = '';
                      var titlefound = 0;
                      for (var i = 0; i < taglength; i++) {
                          if (p.tags[i].search(/author/i) != -1) {
                              author = p.tags[i].replace('author:', '');
                              authorfound = 1;
                          } else if ((p.tags[i].search(/author/i) == -1 && (authorfound != 1))) {
                              author = 'Guest Poster';
                              authorfound = 0;
                          }
                          if (p.tags[i].search(/title/i) != -1) {
                              title = p.tags[i].replace('title:', '');
                              titlefound = 1;
                          } else if ((p.tags[i].search(/title/i) == -1 && (titlefound != 1))) {
                              title = '';
                              titlefound = 0;
                          }
                      }

                      if (p.type == 'photo') {
                          text += '<!-- photo --><h3>' + title + '</h3>';
                          if (p.photos.length > 1) {
                              text += '<div class="liveblog_gallery">';
                              for (var x in p.photos) {
                                  text += '<figure><a href="' + p.photos[x].original_size.url + '" class="fancybox" rel="gallery-' + p.reblog_key + '"><img src="' + p.photos[x].alt_sizes[1].url + '"></a>';
                              }
                              text += '<figcaption><p>' + p.caption + '</p></figcaption></figure></div>';
                          } else {
                              text += '<figure><img src="' + p.photos[0].alt_sizes[1].url + '"><figcaption><p>' + p.caption + '</p></figcaption></figure>';
                          }
                      } else if (p.type == 'text') {
                          text += '<!-- text --><h3>' + p.title + '</h3>' + p.body;
                      } else if (p.type == 'video') {
                          if (p.video_type == 'youtube') {
                              text += '<!-- youtube video --><h3>' + title + '</h3><div class="video-container">' + p.player[2].embed_code + '</div>' + p.caption;
                          } else {
                              text += '<!-- video --><h3>' + title + '</h3><iframe width="700" height="394" frameborder="0" webkitallowfullscreen="" mozallowfullscreen="" allowfullscreen="" data-height="394" data-width="700" data-can-resize="" data-can-gutter="" scrolling="no" class="embed_iframe tumblr_video_iframe" style="display: block; background-color: transparent; overflow: hidden; width: 100%; height: 394px;" src="https://www.tumblr.com/video/<?php echo $liveblog_tumblr_url; ?>/' + p.id + '/700/"></iframe>';
                          }
                      } else if (p.type == 'quote') {
                          text += '<!-- quote --><blockquote><p>&ldquo;' + p.text + '&rdquo;</p><cite>&mdash; ' + p.source + '</cite></blockquote>';
                      } else if (p.type == 'link') {
                          if (!p.excerpt) {
                              var excerpt = '';
                          } else {
                              var excerpt = '<p>' + p.excerpt + '</p>';
                          }
                          if (!p.link_image) {
                              var link_image = '';
                          } else {
                              var link_image = '<a href="' + p.url + '" target="_blank"><img src="' + p.link_image + '"></a>';
                          }
                          if (p.publisher == 'instagram.com') {
                              social_title = p.title.split(':');
                              social_handle = p.title.split(' ');
                              text += '<!-- instagram link --><figure>' + link_image + '<figcaption><p>' + p.excerpt + '<br>&mdash; <a href="' + p.url + '" target="_blank">' + social_title[0] + '</a></p></figcaption></figure>';
                          } else if (p.publisher == 'twitter.com') {
                              social_title = p.title.split(' on ');
                              social_handle = p.url.split('/');
                              if (p.excerpt != null) {
                                  var excerpt = p.excerpt.replace(/(https?:\/\/[^\s]+)/g, "");
                              }
                              text += '<!-- twitter link --><blockquote><p>' + excerpt + '</p><cite>&mdash; <a href="' + p.url + '" target="_blank">' + p.title + '</a></cite></blockquote>';
                          } else {
                              if (!p.link_image) {
                                  text += '<!-- link --><h3><a href="' + p.url + '" target="_blank">' + p.title + ' &raquo;</a></h3>' + excerpt + p.description;
                              } else {
                                  text += '<!-- link --><figure>' + link_image + '<figcaption><h3><a href="' + p.url + '" target="_blank">' + p.title + ' &raquo;</a></h3>' + excerpt + p.description + '</figcaption></figure>';
                              }
                          }
                      }
                      var dts = new Date(p.timestamp * 1000);
                      var n = dts.toLocaleTimeString();
                      var p = dts.toLocaleDateString();
                      text += '<div class="liveblog_timestamp">Posted by ' + author + ' on ' + p + ' @ ' + n + '</div>';
                      text += '</li>';

                  }
                  $('ul.liveblog_entries').html(text);
                  var result = 0;
                  result = posts.response.total_posts / 5;

                  if (result <= 1) {
                      $('.liveblog_nav').remove();
                  } else {
                      $('.liveblog_nav_pages').nextAll().remove();

                      var nav = '';
                      if (currentpage != 1) {
                          nav += '<div class="navright"><a href="?tumblrpage=' + (+currentpage - 1) + '">Newer &raquo;</a></div>';
                      }
                      if (currentpage != Math.ceil(result)) {
                          nav += '<div class="navleft"><a href="?tumblrpage=' + (+currentpage + 1) + '">&laquo; Older</a></div>';
                      }
                  }
                  $('.liveblog_nav').html(nav);


              },
              complete: function () {
                  setTimeout(repeatAjax, 300000); // After completion of request, time to redo it after 5 minutes (in milliseconds)
              }

          });
      }
<ul class="liveblog_entries"></ul>
<div class="liveblog_nav"></div>