Since 7 out of every 12 people are bored by cable news, 5 out of every 12 people are not bored by cable news. This means that there are 5/12 * 280 = 116 people at the convention who are not bored by cable news. Therefore, there are 280 - 116 = 164 people at the convention who are bored by cable news. So the answer is 164