It should. The DVD drive I got is 5.8x1.6x6.7, and it fits perfectly in my 5.25" bay. I honestly couldn't tell you why it's called a 5.25" bay though.
Awesome, thanks!
Apparently the name 5.25" has to do with the size of the floppy disks the drives were made around.
Here's my tentative shopping list...
CPU: i5 4670 (26,590 yen)
Motherboard: ASUS H87-Pro (9,504 yen)
RAM: 8GB DDR3 1333 or 1600 (about 8,000 yen)
SSD: Crucial CT120M500SSD1.PK01 120 GB (8,400 yen)
Storage: Western Digital WD20EZRX 2TB (7,780 yen)
Power supply: RAIDER RA-650 (7,580 yen)
Case: Zalman Z9 U3 (5,439 yen)
Optical drive: LG Electronics BH14NS48 (7,860 yen)
Total: about 82,428 yen
Graphics: maybe later, or a SAPPHIRE R7 260X (20,050 yen)
Windows 7 license, mouse, keyboard, speakers, monitor, wireless adapter, and external HDDs will be carried over from the last machine.