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: for package: rsyslog7-7.4.10-3.el6_6.x86_64
--> Processing Dependency: 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           
 rsyslog7        x86_64        7.4.10-3.el6_6   rhel-6-server-rpms    1.3 M         
 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]:                                                                

By karlo