A simple answer to your question - No, the installer/restore from a MacBook Pro will not install on any MacBook.
However, you CAN boot from that DVD, and transfer the older hard drive + files to your new hard drive - using the restore function in the Disk Utility. You can do that same thing without any startup DVD. Swap the hard drives. Put your old hard drive in an external case, and boot from THAT hard drive. Open your Disk Utility, click the restore tab. Drag your old hard drive into the source line, and drag your new hard drive (after you format it for MacOS Extended (Journaled)) into the Destination line - and finally, click the Restore button, and give it time to complete, which might take an hour or two.
When that is complete - set your boot drive to your new hard drive in your System Preferences. And, restart.
Then, run your Software Update until your 10.5 system is fully up-to-date.
If, OTOH, if you are replacing the hard drive because your old hard drive has failed, then you need an installer DVD that will work... You can purchase a 10.6 (Snow Leopard) installer for only $30 - and be ready for Lion (another $30
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) when Apple releases that sometime this month! That's assuming the you have a Core2Duo processor - and not the oldest CoreDuo, which won't take Lion.