Do you have any idea of the failure rate of the V2? It was hideous! Way to many exploded or crashed at launch. The A12 never became operational. Navigation, from the European coast to England targets was at best "problematic". At best. Now, navigation from orbit at TL5?
How would maned re-entry work? Where, seriously, given the TL5 equipment, would you safely retrieve an astronaut? Or find him/her/them?
NASA benefited greatly (more than greatly, as did the Russian program) from the captured German scientists and engineers, but, the first manned flights were far from TL5.
Honestly, I'm not trying to stifle your creative thoughts, but you need a better example to support your contention that the one given. Just wait till TL6?