Out of memory in MySQL error log
A 32-bit MySQL on a 64-bit OS in 8GB of RAM:


The OS can access all 8GB.
The 32-bit MySQL is given no more than 4GB; it is impossible for it to use more than that.  Actually, it can't quite use all 4GB.
You could (should) reconfigure MySQL (via my.cnf) as if it were on a 4GB machine.
You could get a 64-bit version of MySQL
You could upgrade MySQL -- 5.0 is really antique.  Even 5.1 is 'dead'.  There is 5.5, rapidly aging, 5.6, 5.7, and soon 8.0.


More on configuring memory:  http://mysql.rjweb.org/doc.php/memory