In Audacity you have to check the 'Use custom mix' radio button in the Import/Export section of the preferences. This will let you export multi-channel files, and manually assign tracks to channels.
Other than that, plain old .wav works fine for this.
But you can also use SoX to create the files in a more automated manner.
Manually you can combine (or 'merge' as it's referred to in the documentation) five distinct files into a single five-channel file like this:
sox -M chan1.wav chan2.wav chan3.wav chan4.wav chan5.wav multi.wav
To automate the process I put together a short Bash routine for producing a multichannel file with staggered test tones:
NUM=5 # Number of channels
LEN=2 # Length of each test tone, in seconds
OVL=0.5 # Overlap between test tones, in seconds
# A one-channel base file containing simple white noise.
# faded at both end with a quarter wave envelope to ensure
# smooth equal power transitions
sox -n -b 24 -c 1 out.wav synth $LEN whitenoise fade q $OVL -0 $OVL
# Instead of white noise you can for example make a 1kHz tone
# like this:
# sox -n -b 24 -c 1 out.wav synth $LEN sine 1k fade q $OVL -0 $OVL
# Or a sweep from 10Hz to 10kHz like this:
# sox -n -b 24 -c 1 out.wav synth $LEN sine 10-10k fade q $OVL -0 $OVL
# Produces a sequence of the number of seconds each channel
# shall be padded with
SEQ=$(for ((i=1; i<=NUM; i++))
do
echo "$i 1 - [$LEN $OVL -]x * p" | dc # reverse-Polish arithmetic
done)
echo $SEQ
# Padding the base file to various degrees and saving them separately
for j in $SEQ
do
sox -c 1 out.wav outpad${j}.wav pad $j
done
# Finding the just-produced individual files
FIL=$(ls | grep ^outpad)
# Merging the individual files into a single multi-channel file
sox -M $FIL multi.wav
rm $FIL # removing the individual files
# Producing a multi-channel waveform plot
ffmpeg -i multi.wav -y -filter_complex "showwavespic=s=2400x900:split_channels=1" -frames:v 1 waveform.png
# displaying the waveform plot
open waveform.png
As the waveform plot clearly shows, the result consists of a file with five channels, each with the same content, just moved about some in time:

More on reverse-Polish arithmetic using dc
: http://wiki.bash-hackers.org/howto/calculate-dc
More on displaying waveforms using ffmpeg
: https://trac.ffmpeg.org/wiki/Waveform