first fighter of the row is I-301 (fighter 301, 301 is the number of plant where design bureau was based)
later it was renamed to LaGG-1 after S.A.Lavochkin, V.P.Gorbunov, M.I.Gudkov.
however, LaGG-1 (with M-105P) was a test variant and after debugging and improvements serial plane was named LaGG-3 (still with M-105P).
having quite a heavy structure, LaGG-3 was underpowered, and in fighting this factor, an new power plant was sought, separatedly by Gudkov (with Gu-82 project of LaGG-3 with M-82), and later Lavochkin (with the same M-82).
however, a serial one become design of Lavochkin.
in documents about preparation of production it was named LaGG-3 with M-82, sometimes LaG-5 (with probable presence of Gorbunov).
early series had the very same airframe (and canopy) as LaGG-3, but nor Gudkov, neither Gorbunov are related to this design (afaik).
La-5 index appeared since 1942-04.
1942-09-08 index LaG-5 cancelled and replaced by La-5.
so by the time LaGG-3/M-82 came into extended action it was already La-5.
therefore i doubt that 'end user manual' can have index LaG-5.