You want to install rsyslog7 but you get:
Error: rsyslog7 conflicts with rsyslog-5.8.10-10.el6_6.x86_64
So you choose to erase/remove rsyslog first, but this removes:
cronie, cronie-anacron, crontabs, redhat-lsb, redhat-lsb-compat, redhat-lsb-core, redhat-lsb-graphics, redhat-lsb-printing, rsyslog-relp, sysstat
The solution is to use yum shell (EDIT: OR USE YUM SWAP)
# yum shell
Loaded plugins: security
Setting up Yum Shell
> install rsyslog7
Setting up Install Process
> remove rsyslog
Setting up Remove Process
> run
--> Running transaction check
---> Package rsyslog.x86_64 0:5.8.10-10.el6_6 will be erased
--> Processing Dependency: rsyslog = 5.8.10-10.el6_6 for package: rsyslog-relp-5.8.10-10.el6_6.x86_64
---> Package rsyslog7.x86_64 0:7.4.10-3.el6_6 will be installed
--> Processing Dependency: libjson-c.so.2()(64bit) for package: rsyslog7-7.4.10-3.el6_6.x86_64
--> Processing Dependency: libestr.so.0()(64bit) for package: rsyslog7-7.4.10-3.el6_6.x86_64
--> Running transaction check
---> Package json-c.x86_64 0:0.11-11.el6 will be installed
---> Package libestr.x86_64 0:0.1.9-2.el6 will be installed
---> Package rsyslog-relp.x86_64 0:5.8.10-10.el6_6 will be erased
--> Finished Dependency Resolution
======================================================================
Package Arch Version Repository Size
======================================================================
Installing:
rsyslog7 x86_64 7.4.10-3.el6_6 rhel-6-server-rpms 1.3 M
Removing:
rsyslog x86_64 5.8.10-10.el6_6 @rhel-6-server-rpms 2.1 M
Installing for dependencies:
json-c x86_64 0.11-11.el6 rhel-6-server-rpms 51 k
libestr x86_64 0.1.9-2.el6 rhel-6-server-rpms 19 k
Removing for dependencies:
rsyslog-relp x86_64 5.8.10-10.el6_6 @rhel-6-server-rpms 21 k
Transaction Summary
=======================================================================
Install 3 Package(s)
Remove 2 Package(s)
Total download size: 1.3 M
Is this ok [y/N]: