I understand this sentence as meaning "Touya will lose! At this rate he will not last 5 minutes" but I am puzzled as to why と is used here
With a direct search i see that "と持たずに" is not only a used phrase, but it seems to always be used with time expressions. However I don't know what sort of と this is, and a phrase like （５分）と持つ doesn't seem to exist. In fact a phrase like 'last 5 minutes' seems to be ５分持つ without any particle, so I am a little lost.
I wondered if I should interpret it as a conditional と, so that the meaning is something like "five minutes like this and he will not last" but I am pretty sure that is not right.
Any help would be appreciated.