Of the two species mentioned in the question, hexacoordinate nitrogen(V) (the Roman numeral V means oxidation state, not formal charge) is the better established case in prospective crystals. No compound having this nitrogen state is known experimentally, but theoretical calculations predict a nitrogen-pentafluoride salt containing $\ce{NF6^-}$ at high pressure[1]theoretical calculations predict a nitrogen-pentafluoride salt containing $\ce{NF6^-}$ at high pressure[1]. The proposed hexacoordinate nitrogen(V) radius is likely based on this calculation.
Pentacoordinate nitrogen, in a lower oxidation state, has been experimentally obtained in an organic complexPentacoordinate nitrogen, in a lower oxidation state, has been experimentally obtained in an organic complex[2].
References
Kurzydłowski, D., Zaleski-Ejgierd, P. "Hexacoordinated nitrogen(V) stabilized by high pressure". Sci Rep Kurzydłowski, D., Zaleski-Ejgierd, P. "Hexacoordinated nitrogen(V) stabilized by high pressure". Sci Rep 6, 36049 (2016). https://doi.org/10.1038/srep36049.6, 36049 (2016). https://doi.org/10.1038/srep36049
Chenting Yan, ORCID logo a Masato Takeshita,a Jun-ya Nakatsuji,a Akihiro Kurosaki, Kaoko Sato,Rong Shang, Masaaki Nakamoto Yohsuke Yamamoto, Yohei Adachi, Ko Furukawa, Ryohei Kishid and Masayoshi Nakano. "Synthesis and properties of hypervalent electron-rich pentacoordinate nitrogen compounds". Chem. Sci., 2020, Chenting Yan, ORCID logo a Masato Takeshita,a Jun-ya Nakatsuji,a Akihiro Kurosaki, Kaoko Sato,Rong Shang, Masaaki Nakamoto Yohsuke Yamamoto, Yohei Adachi, Ko Furukawa, Ryohei Kishid and Masayoshi Nakano. "Synthesis and properties of hypervalent electron-rich pentacoordinate nitrogen compounds". Chem. Sci., 2020, 11, 5082-5088. https://doi.org/10.1039/D0SC00002G.11, 5082-5088. https://doi.org/10.1039/D0SC00002G.