Unfortunately, it is going to be the traditional stir and heat method : )
I believe most people make 0.5M stock solution and once you have that, your 5mM is easy peasy.
As for the 0.5M stock, you would want to use 10N NaOH for pH adjustment, else you will "run out" of volume for the buffering. You want to start adding the NaOH because the EGTA would only dissolve at pH8.0. I don't remember it being excessively difficult the last time I did.
So, in terms of steps:
1. Fill your container with final volume required and add a stir bar.
2. Mark off the volume on the container and pour out about 30% of the solvent.
3. Weigh EGTA and add to solvent.
4. Start to stir and heat. Nothing much is going to happen.
5. Place your calibrated pH probe into the suspension and keep it there.
6. Start adding drops of 10N NaOH slowly to the mixture.
7. The crystals should dissolve close to pH8.
8. Once all the crystal dissolve, remove the pH probe and top up the volume to your marked level in step 2.
Note: EGTA will not go into solution without NaOH. Once the pH has been raised sufficiently it dissolves quickly. For pH 7.5 the exact amount required is slightly above 4g. Add 3.5-4g immediately, then proceed carefully not to overshoot the desired pH.