The train hasn't run to Lab City for about 15 years, well the ore train still operates but no passenger service. To access the headwaters of the Moisie you can still take the passenger train and get off at Emeril Junction and arrange a shuttle to Lab City (about an hour drive). Alternative is to drive to Lab City (nice drive). It may still be possible to ship a vehicle by rail back to Sept-Isle, I did that in 2007, no idea if it's still possible.
Another alternate is to take the train and get off at Oreway, paddle across Ashuanipi Lake and portage over to Lac Menistouc. You can also access via the Riviere Aux Pekans from Hwy 389 about an hour south of Fermont/Lab City.
None of these routes could be done in 5 - 7 days, 10 if you are a REAL speed demon, 15/16 days if you move quickly and 18+ if you want to enjoy the trip.
Note that there was a massive fire in the upper river in 2013, there have been few reports from paddlers after that date although I'm sure some have done it.
I don't think there is any feasible or worthwhile 5 - 7 day trip.
You can search the archives here, there are many posts about the Moisie from the 00's. Detailed maps available from cartes plein aire:
http://www.cartespleinair.org/Canot/cartes.html