Lightroom 5 evaluation finished. How to license single product without CC? And without downloading software again?

you need to uninstall your cc version and install the perpetual license version.

after uninstalling, you should clean (Use the CC Cleaner Tool to solve installation problems | CC, CS3-CS6), then install lr 5.7.1.

Downloads available:

• Suites and Programs:  CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4 | CS3
• Acrobat:  XI, X | 9,8 | 9 standard
• Premiere Elements:  13 |12 | 11, 10 | 9, 8, 7
• Photoshop Elements:  13 |12 | 11, 10 | 9,8,7
• Lightroom:  5.7.1| 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'.

window using the Lightroom 3 link to see those 'Important Instructions'.