Yes, yes, just jump 5k lightyears and kill yourself, such grand gameplay, regardless of how you try to defend it, it really is a stupid requirement. 5k in lifetime jumps sounds like a lot but would be gained from actual gameplay from ANYONE, much better than the garbage that he is now.
I travelled 6,700ly yesterday in a 54ly ship, FSSing every system. A lot of that was Neutron jumps but I was in a place & needed to get to another place to meet a friend. I had a reason to do it.
You have a reason to do it, and a reason to not do it (you have never done it before). That, it seems to me, is currently a step too far for you, it makes you frustrated at the thought of it, so imo leave it for now, and try a shorter trip to a nearby nebula or something. Build up to it, keep your targets feeling achievable based on your current experience and each time, aim to better your previous best.
Stay in the stretch zone. 5000ly really isn't that far, and won't really take all that long and once done you won't have to do it again if you don't want to, but you will know what it took to do it & maybe will have pushed your character outside your comfort zone & learned a little about what else the game has to offer. I don't see that as a bad thing
Or you can cheese it & park on somebody's carrier while they take you, feeling superior because you beat the system without learning a damned thing
G5 drives are great, I have G5 Dirty Drag drives on nearly every ship, even exploration builds. How you choose to play is up to you.