Not really. With the launch of Athlon 64, AMD basically replaced all their 32bit CPUs lineups with that new arch, and not kept them along much longer as a lower tier part. By 2005 I expect 90% of new PCs sold were already 64 bit ready.
You're several years off:
"The FIRST processor to implement Intel 64 was the multi-socket processor Xeon code-named Nocona in June 2004. In contrast, the initial Prescott chips (February 2004) did not enable this feature."
"The first Intel mobile processor implementing Intel 64 is the Merom version of the Core 2 processor, which was released on July 27, 2006. None of Intel's earlier notebook CPUs (Core Duo, Pentium M, Celeron M, Mobile Pentium 4) implement Intel 64."
https://en.wikipedia.org/wiki/X86-64#Intel_64
"2012: Intel themselves are limiting the functionality of the Cedar-Trail Atom CPUs to 32bit only"
https://forums.tomshardware.com/threads/no-emt64-on-intel-at...
Intel had 80% of the CPU market at the time.
So you could very well have bought a decent quality 32 bit system after 2005, although the writing was on the wall long before then.