I suggest that you download and install LR 5.7.1 from the following website. It's the last update that will be released for Lightroom 5.
Also, you may be reading the notification that was released last week indicating that there was new software available for Lightroom. That is not an update for Lightroom 5. It's worded poorly, but it's referring to Lightroom upgrades that must be purchased. The link I provided will enable you to update Lightroom 5, but you will still receive that "new software" notification unless you click on the ignore button in the lower left-hand corner.
The popup is sending you to a page to upgrade to LR 6/CC.
Use Jim’s link to get the last update for LR 5: 5.7.1, from mid-December.
These instructions assume you have the serial-number-activated LR 5 and that you don’t want to pay for the upgrade to LR 6/CC..