I guess you mean LO 5.1.0.3.
I had the same problem
The verification took a long time and my computer got almost completely unresponsive.
Activity Monitor indicated that kernel_task had grown to more than 6.3GB (real memory). My machine has 8GM memory. It did not take very much CPU time, but everything came virtually to a halt. Even the clock sometimes lagged minutes behind. The verification process took more than 2 hours and 15 minutes, after which I had to leave. When I returned it had finished, so I know it took less than 5 hours. Ater confirming that I wanted to run the application downloaded from the internet, LO continued, but it took at least 10 minutes before it appeared. In the meantime the kernel_task memory footprint still was high, but later it dropped back to more reasonable values.
I did this twice, with a reboot in between. The reboot didn't solve the problem.
I also tried LO 5.0.5, and its verification took about 5 minutes (still quite long I think), with kernel_task going up to about 4GB. But at least the system continued to work normally.
So it seems there is something fishy with LO 5.1.0.3
Same issue here
I have just successfully installed LibreOffice 5.1.4 on OSX El Capitan 10.11.5, with no sign of these verification problems. I don't know whether that's a result of a change in LO or OSX.
Same problem with 5.1.4 on MacBook Pro (2015) with MacOS 10.10.5
It seems the problem is still NOT SOLVED (as of July 26th 2017), despite several tickets marked "doubled", hence solved: MBP late '11, 2,5 GHz Intel Core i7, 16 GB RAM, Mac OS 10.10.5 Yosemite.
After installing LO 5.3.4.2 it wouldn't start, hanging first with verification when installing German language pack, after I tried without - same result. "xattr -d" worked, but still ... LO 5.3.4 is 3x slower than LO 4.4.5.2 (startup, format cells...). I returned to the older version, works fine.
LO V 6.2.1 + OSX V 10.10.5 has the same problem, i.e. "verification" hangs up at the end of the installation of certain apps.
The workaround for me* is to go to system preferences/security & privacy/general and to temporarily set "Allow apps download from" to "Anywhere". The other two selections wouldn't cut it. Don't forget to return to the original settings after having completed your installations!