You can certainly make pentanitrophenol but it is way more harder to get the -NO2 group to occupy the last remaining m-places. Historically, it has been achieved previously in the early 1900s but the way to synthesis was not straightforward. They had to make many observations, understand the chemical behavior, analyze, assume things and then come to a conclusion. They have to start with halogen substituted aniline and phenol. They didn't know how the nitric acid will behave towards nitrated m-derivates of aniline and phenol and they understood that there was no way the extra -NO2 can be wedged in between o- and p- position. The only exception noticed was tetranitrophenylmethylnitramine discovered in 1889 which was obtained by direct action of fuming nitric acid on two different trinitrophenyldimethylanilines. They observed that the -NO2 group placed at the m-position is very mobile and very liable to substitutition.
Later they achieved tetranitrophenol by oxidizing oximes. In the same way, they subjected m-nitro and m,m-dinitromethylaniline with conc. nitric acid and proved that it is possible that the pentanitro- derivative is possible along with the tetranitro- derivative. Finally, came to m-nitro and m,m-dinitrophenol where they subjected them with conc. nitric acid and it formed the tetranitro and pentanitrophenol as they predicted (m.p 140 °C and 190 °C resp.).
Once they achieved this, they went ahead and achieved nitrating m-substituted phenol where the substituted group is something beside -NO2 group.
All of their findings can be found in the below journals:
- On pentanitrophenylmethylnitramine and tetranitro and pentanitrophenol by Dr. J.J. Blanksma, 1901
- Nitration of meta substituted phenols by Dr. J.J. Blanksma, 1906