Jokova,
You could try repairing disk permissions: Applications>Utilities>Disk Utility, select the top disk on the left-hand side and click "Repair Disk Permissions".
It might be a RAM issue, although*if you have at least 2Gb and it is seated properly, it probably won't be this.
Have you installed any outdated control panels/utilities which might be causing some conflict with 10.5? Some older Applications and their extensions can also cause issues.
Have you got any anti-virus software? This has a tendency to cause more trouble than it's worth on the Mac.
Applemacster