I would not disagree that you can do it, but I am skeptical that you can do it in 5 years.
Honda did develop their HF118 turbofan engine apparently from scratch, but it took about 8 years [1]. And for the actual commercialization they teamed up with GE and then it took another 10 years until certification of the successor HF120 [2].
There's a world of difference between 2000 lb and 20,000 lb thrust though. And as you mentioned, they teamed up with GE in the end because, to be frank, turbojets are just hard.
Honda did develop their HF118 turbofan engine apparently from scratch, but it took about 8 years [1]. And for the actual commercialization they teamed up with GE and then it took another 10 years until certification of the successor HF120 [2].
[1] scroll down on https://global.honda/en/tech/eVTOL_gas_turbine_hybrid_system...
[2] https://en.m.wikipedia.org/wiki/GE_Honda_HF120