Without knowing your budget or load, I'd think of trying to divide your backup storage to a couple devices, just to offset the network load a little.
I don't know what others would think...I'm not a specialist in databases, and we don't have anything on a huge scale like a terabyte of data + diffs to store and manage, but I'd wonder about adding a second NIC to the database servers and having a separate switch that connects to a couple of servers acting as NAS devices. Have servers 1,2, and 3 go to backup server 1 and servers 4 and 5 go to backup server 2 on the second LAN. that should ease some of the network congestion, and having separate machines may help alleviate some of the burden on the drives and drive throughput.
I'd also consider getting external drives attached to the servers so you can save it to a "local" drive, then you can pull data from the physical external disks to another system for a direct copy and not saturate a nic or switch. It requires physical intervention, though, and couldn't be easily automated (although you could script something that keeps only files/backups of a certain date to keep from overfilling the file system). It would require 5 large external drives, but it may prove faster than saturating your network.
I'm sure others have better ideas, though. This would probably be something to consider entry-level or on the cheap.