Over different versions of OS X, what comes with the OS has gradually migrated from 32-bit-only (through 10.2) to having minimal support for background-only 64-bit apps (10.3 and 10.4), to full support for 64-bit Cocoa apps (10.5), to a full 32/64 OS including the kernel (10.6) to actually starting to drop support for 32-bit mode (10.7 shipped with many 64-bit-only system apps, and will not run on a 32-bit-only CPU). Long answer: OS X doesn't have 32-bit and 64-bit versions it uses a universal binary format which allows programs, system components, etc to be installed with both 32- and 64-bit code, and the system simply picks the 'best' one to use based on the CPU you're on. You can check the CPU with the command sysctl hw.cpu64bit_capable ( 0 means no, 1 means yes) or by looking up the model (if it has a 'Core Solo' or 'Core Duo' CPU it's 32-bit only if it's a 'Core 2 Duo' - note the '2' - it's 64-bit). Short answer: if your model of MacBook has a 64-bit capable CPU, you can run 64-bit apps under 10.5.8.

Apple application support 64 bit