Install MySQL 5.6.21 on Centos 7

Cents is a redhat based system their process is geared towards enterprise and stability over tone such that they major, minor versions of the services, applications available on them is maintained.
Micro and nano updates are applied for sevurity, bug fixes.

To answer your issue, you would need to download the RPM from dev.mysql.com and any dependency to get the version not available on the centos 7.
Debian, Ubuntu are more of a more current version, but you have to copiously look through the changelogs of updates to make sure your deployed application would not be adversely impacted by the update.
I.e. Your app uses functions, tools that the newer version deprecated, the tools are no longer available, Claud or changed how they work......

Leapt to the wrong conclusion, my advice would be fix the issue as it is likely vulnerable .....
And you either do it know potentially with some minor/moderate changes versus delaying it till the next time a couple of years down the line where the disparity be ones a large, major effort and .....

The legacy website is written by a company long long time ago and it is difficult to make changes. I still need MySQL 5.6 installed. I'm sucked in the  following, any idea ?

[root@server html]# rpm -ivh mysql-community-release-el6-5.noarch.rpm
error: Failed dependencies:
        mysql-community-release conflicts with (installed) mysql57-community-release-el7-10.noarch