Unlike many motherboard OEMs, Dell releases BIOS updates that can be executed from linux. Unfortunately, a portion of these updates are precompiled binaries for 32-bit linux only. Here's how I made the BIOS update work for my Precision T5400.
Get the update:
# should be 11a13eae55e01ca5aaadda459b78cf2a
chmod a+x T5400A11.bin
Like many vendors of proprietary software in the world of FOSS, the update takes the form of a short shell script that extracts and unzips a precompiled binary from itself. All the work is done in that binary. Unfortunately, when you try to run it under a 64-bit Debian install, you'll get something unhelpful like:
./flash: No such file or directory
So here's the solution to run this binary under 64-bit Debian:
dpkg --add-architecture i386
aptitude install libc6:i386 libstdc++6:i386 zlib1g:i386
Now you should be able to run the update!