Old Macs are disposable and need to be replaced every 4-5 years.
Not necessarily. It will depend on the Mac. And depends on what you need the Mac to do.
I have a 2009 MBP that still runs great...and can run the latest OS (if I wanted...haven't gotten around to upgrading it...it is still on Lion). It has benefited from removing the optical drive to install an SSD for a boot drive and then upgrading the internal hard drive to a 1.5 TB hard drive and also upgrading the RAM to 8 GB. I do have newer Macs, but not because the 2009 MBP was "disposable", but rather I wanted "new toys" (computers are my one expensive hobby
In the original posters case, OTOH, they are at the point where there is not much that can be done to upgrade that particular Mac model. Upgrading the RAM from 1 GB to 2 GB would not be that expensive and likely would still help (depending on what the original poster needs the Mac to do). As noted by Buddyme2, they cannot upgrade the OS any more, so if they want the newer features of newer OSs, then a new Mac is the only option. The other thing that might help with the speed is to do a re-install of the OS and applications. I would tend to suggest that a new hard drive would not likely help that much.
In the end, it is a function of the Mac, what the person needs that Mac to do, and how much "speedier" someone might need the computer to be.