Space Quest V: The Next Mutation

"The game starts with a dramatic opening and Roger mid-mission on his ship: he is then revealed to be playing in a flight simulator, shaped suspiciously like the Millennium Falcon, at the StarCon Academy. Roger cheats to pass an aptitude test, and he's then given his own command— the garbage scow SCS Eureka, which looks (and functions) like an oversized vacuum cleaner. The game involves several small missions, similar to ones seen in typical Star Trek episodes.

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Source: Wikipedia, "Space_Quest_V:_The_Next_Mutation," available under the CC-BY-SA License.