(In reply to A start...
by Dej Mar)
Your excellent start deserves a small hint:
The words, GET, MY, GIRO and GUMBO are YOUR correct guesses for (W1 W2 W3... W5) OR (W1 W2 .. W4 W5 )- will
not tell you which partial product is W3 and which W4.
The missing word Gxxxx is an English slang word for a nerd, ignorant etc and as you justly remarked does not use any additional letters.
You can either:
1. find the missing word or
2. try to solve the alphametics without one missing product or
3. find the names (assuming nothing esoteric) just by looking
at the sequences of the digits .
I am confident that you will get the right answer.