Do Blu-ray burners have a smaller file size limit like DVD+-Rs? If I buy a BD burner will I be able to use it to back up five and six GB files or will I have to split them up into smaller chunks?
If you select the UDF file system when you burn the disc, you can burn single files up to the limit of the disc capacity. This is also true of DVD+/-R media.
DVD-Video media use UDF version 1.02. These discs contain a so-called UDF Bridge format, whereby both an ISO 9660 (Level 1) and a UDF 1.02 filesystem are present on the same disc, describing the same filesystem. http://en.wikipedia.org/wiki/Universal_Disk_Format
On a DVD-Video disc, the file size restriction is from the ISO 9660 part of the "Bridge" format. DVD video files are generally less than 2^30 = 1,073,741,824 bytes in size, although the format size limit is actually 2^32 - 1 bytes.
If you go pure UDF, it's just the media size. (Technically, it is limited to 2^60 = 1,152,921,504,606,846,976 bytes but there's no media that big yet!)