Your G5 will support larger than 500 GB drives; 500 GB was the largest offered at the time of sale is all.
1TB, 1.5 TB and 2 TB drives are no problem in the G5, but larger than 2.2 TB breaks a capacity limit for APM (Apple Partition Map in formatting is required for boot in a PPC Mac). For use of a 3 TB or 4 TB drive, partition the drive so that no 1 partition is larger than 2 TB. The drive should then have all space available.
Otherwise, for storage only, using Tiger or Leopard, format GPT. These drives (formatted with GPT) are not bootable in a PPC Mac; G3, G4 or G5.
One other potential issue to consider is SATA 3 Gb/s (SATA rev. 2) and SATA 6 Gb/s (SATA rev. 3) related.
The SATA rev. 1 controller of the G5 works well with SATA rev. 2 drives, but is not so friendly with SATA rev. 3 drives. SATA rev. 3 drives from Hitachi (7K series) typically work as is. Drives from Western Digital (Black and Blue series) require a jumper on pins 5 and 6 to limit a SATA 6 Gb/s drive to SATA 3 Gb/s to work well in a G5. If not jumped, the drive is typically not seen.
I wouldn't advise use of any make or model of "green" or 5400 RPM drive.