T5 doesn't change the maximum available in the Post SRW (M1000), Classic (M1100), Rebellion (M1116), Hard TImes (M1120, New Era (M1200), nor "Dawn of the 4th Imperium" (M1250) eras.
It's Implied strongly in T5.09 that while the TL minimum must be met, meeting the TL minimum isn't sufficient in and of itself to develop the various FTL drives. (p 334)
J7 isn't available (IIRC what Marc said in a draft) until about 1400 [g="Third Imperium Calendar]3IC[/g].
H1 isn't available until shortly prior to 1900 3IC. And, despite some TL 20+ worlds, it won't have S1 in that timeframe, either.
Likewise, Drop Tanks aren't developed until after the SRW, and not commercially available until around the 5FW. The tech, however, is about TL 9...
And further, J7/8/9 have rather impressive fuel requirements until one converts to Antimatter slugs... which cut the fuel to (Jn)%