Disparity between training and testing errors with deep learning: the bias-variance tradeoff and model selection
Your question is, what model is better between one that seems more overfitted (larger difference between train and eval set) but it has also higher scores or one that has less variance between train and eval set but at the same time it has worst results. Everything assuming that you have done a correct train test split and there is no data leakage and distributions keep the same in every split (this is important to check).

There was a discussion about this some time ago. The answer seems to be kind of subjective since the quantitative analysis has been performed

Normally there is the following trade-offs:


Complexity: Occams razor and complexity vs interpretability. In your case, both models are almost with the same complexity (it's not a linear regression against DL, just a couple layers more) and the interpretability stays the same,
Generalization. You want your model to behave in the best possible way in production, an overfitted model in train seems to have more probable cause to fail due to a change of distribution in production. 


You only have 3 data points so it's hard to say what it will be best. My suggestions will be that:


Add some more layers (6,7,8) just to see when your test results start to go down (you can still overfit much more) and then visualize the data and keeping both concepts defined before choosing what are the best architectures for your model
Investigate with more parameters (adding one more layer seems to be a high difference hyperpameter), like learning rate, layer size, activations functions and so on... 
Consider using one of the famous architectures for your problem, they are developed in every framework and tested by a lot of people, they are there because the seem to be the best at their task, give them ago. There has been already a lot of electricity wasted in deep learning hyperparameter tunning.