I've found Illusie's redaction of **Grothendieck's original notes for SGA 5 Exp II**:

[Formules de Künneth pour la cohomologie à supports propres, par L. Illusie (d'aprés des papiers secrets de A. Grothendieck.][1] 

It's a very heavy file (1.6 GB). You can instead look at each page by clicking on the jpgs of [this page][2].


  [1]: https://repo-archives.ihes.fr/FONDS_GROTHENDIECK_ILLUSIE/FG_IL_5_Ecrits_Mathematiques_SGA/3/FG_IL_5_SGA5/FG_IL_5_SGA5/FG_IL_5_SGA5.pdf
  [2]: https://repo-archives.ihes.fr/FONDS_GROTHENDIECK_ILLUSIE/FG_IL_5_Ecrits_Mathematiques_SGA/3/FG_IL_5_SGA5/FG_IL_5_SGA5/