MacBook Pros newer than October 26, 2007 can't use the retail disc called 10.5 (10.5.1, 10.5.4, and 10.5.6 were later retail discs). Retail discs
have this image on them:
MacBook Pros newer than December 14, 2008 can't use the retail disc called 10.5.6, and if older than August 28, 2009, could only use the 10.5 installer disc pre bundled with them called MacBook Pro.
MacBook Pros that are newer than August 28, 2009 can't run Mac OS X 10.5.
If you have a Mac newer than March 14, 2010, you need the original installer discs that came with your Mac.
If you have a Mac newer than July 19, 2011, boot with command-R to enable network install of the operating system. Note, these Macs did not come with installer discs when bought new from Apple.
Some older Macs that had a firmware update on them also support command-R network install of an operating system.
Both would require some internet connectivity.
Note "newer" means the model either had a hardware refresh on or after that date, or had a hardware change.
If your old hard drive is still accessible, you should be able to boot off it, if it sits in an enclosure or hard drive docking station capable of mounting its ports.
Lastly if you got the hard drive from a non-Apple source, it likely needs to use the Disk Utility on the installer software to format with GUID partition formatting before you install the operating system. Note, such formatting will wipe the hard drive, unless you already have a separate partition you have allocated for another operating system. Installing an operating system will negate any operating system already there, and if it is older than the operating system already there, could make the system more unstable, if it is newer, software that ran on the older operating system may not run at all on the newer. So know what you have on the hard drive, and know what you used before.