If you don’t own Traveller 5 yet, then you should have a look at this. This is Traveller 5 as it should have been. Three books, and “complete with errata and a handful of useful upgrades!”
https://www.kickstarter.com/projects/traveller5/traveller-fifth-edition
I already have T5, but this looks so good that I am thinking about backing this.
How is (or would you think) this Traveller different from Mongoose Traveller 1st and/or 2nd edition? (I’m currently playing in a 2nd edition game and own 1st edition.)
You can probably play in a similar way, but there is so much more in Traveller 5. Lots of generator rules for everything. Also lots of charts.
There are to many things to explain in a comment.
Have a look here:
http://wiki.travellerrpg.com/Versions_of_Traveller
and here:
https://zhodani.space/2013/05/19/t5-review/