that link is the only one for pre cc app updates.
is the current downloadable version cs5.04? if yes, that would explain why there is no update for the downloadable version. you would uninstall your cs5 and install the current download in that situation.
if the current downloadable version is not cs5.04, contact adobe for clarification, http://helpx.adobe.com/x-productkb/global/service1.html
Downloads available:
- Suites and Programs: CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4 | CS3
- Acrobat: XI, X | 9,8 | 9 standard
- Premiere Elements: 12 | 11, 10 | 9, 8, 7
- Photoshop Elements: 12 | 11, 10 | 9,8,7
- Lightroom: 5.6| 5 | 4 | 3
- Captivate: 8 | 7 | 6 | 5
- Contribute: CS5 | CS4, CS3
Download and installation help for Adobe links
Download and installation help for Prodesigntools links are listed on most linked pages. They are critical; especially steps 1, 2 and 3. If you click a link that does not have those steps listed, open a second window using the Lightroom 3 link to see those 'Important Instructions'.