It does seem that the other answers fail to address the question you have asked.
Is it possible to re-wire car speakers (model JBL GT7-5) to a headphone jack (3,55 mm streo plug) directly without an amp?
The short answer is no, you cannot connect a speaker that size to a headphone jack and expect to hear much sound; you also risk damaging the headphone amplifier if it is not short circuit protected.
This leads to the next question
And if not, what do I need to-do?
You need to add an amplifier between the headphone output and the speaker.
There are plenty to choose from out there, as you are new to electronics, I suggest to get one that is enclosed and has its own power supply.
The key points to look out for are:
- Output Impedance, this must be able to drive 4 Ω speakers, otherwise you will risk damaging the amplifier
- Output Power, avoid amplifiers with a power output higher than the power that the speakers can take, or you will risk damaging them at high volume.
It will be up to you to decide if you want the amplifier to be battery or mains powered.
Here below is a simple schematic of how to connect the amplifier
simulate this circuit – Schematic created using CircuitLab