The advice Allen suggested for an upgrade of the hardware (RAM and replacement battery) in the device is the best route; since another layer of applications that run randomly in the background of an otherwise limited hardware machine can't do it any good. And cleanmymac, mackeeper, etc have successfully been proven to be worse than worthless to any version of Mac OS X no matter the vintage.
Your expectation of the vintage PowerPC G4 architecture is well beyond its ability.
If you get and use programs that hamper the efficiency of the OS X and how it works, then it would be even slower; and the best action would be to add correct quality RAM from a reputable vendor who has experience testing and will guaranty the products they sell will work in your computer. And try to get a replacement new battery so the CPU won't default to a lower processor speed.
https://www.google.com/#q=Mac+OS+X+10.5+PPC+runs+slow
Read up on the correct care of the Mac OS X and keep in mind the current support for secondary product lines such as iPhone, iPad, iPod, and others will not happen with a vintage or obsolete product. Look for a later Intel-based MacBook (a MB/Pro or Air, if new) since they were built to run OS X after Leopard 10.5.8. To use a modern iPhone or iPad, or access the App Store, you'd need at least Snow Leopard 10.6.8. Not a vintage PowerPC G4 notebook. If you had the OS X install DVD for 10.5, and other application install discs, then maybe a fresh total re-install may be helpful. But be sure you can actually go forward with it. (Ideally, you may need to make it run as good as it can, then buy a last model basic MacBook (2006-2010 vintage, see mid-2010 for recent OS X compatibility.)
http://www.everymac.com/systems/apple/powerbook_g4/index-powerbook-g4.html
To clean up a computer, look to the myths, legends, and methods of maintaining the system(s) involved. An active participant usually researches the interrelationship between cause and effect. The user slows down the computer from its original state; it may have seemed fast in its day, and likely was, to a degree.
http://www.thesafemac.com/tech-guides/
I'm sure some of us who've been using computers for more than 20 years, do some reading and have repaired a few dozen computers, and have a life outside of trolling the forums, have some ideas.
PS: there is no upgrade for iTunes in the PowerPC Mac or for Leopard 10.5.8.
Good luck & happy computing! 🙂