Recent versions of Pages and this includes v10.3.2 through v10.3.9 on Catalina have a notion of unsupported hardware models. So even if you are running a current version of Pages, the age of the hardware will take precedent and block Pages from opening the document. A ten-year-old Mac certainly qualifies as unsupported hardware, and certainly appears on Apple's worldwide vintage and obsolete product list.
I would still think that a Pages '08 or Pages '09 document should still open on your aging Mac hardware, provided that the document did not contain features of those Pages applications that are not implemented in the later Pages versions.