All zabbix daemons start with priority "5" as hardcoded in the sources.
See revision 228 dated from 2001-10-01.
That was Zabbix 1.0alpha12

Would be nice to remove this code, which allows to control priority at init scripts level.
Currently default priority for daemons and other process in Linux is "0" so the priority "5" it's sort of "outdated" feature.

#ifdef HAVE_SYS_RESOURCE_SETPRIORITY
if (0 != setpriority(PRIO_PROCESS, 0, 5))
zbx_error("Unable to set process priority to 5. Leaving default.");
#endif