What are the consequences of not freezing layers in transfer learning?
I think that the main consequences are the following:


Computation time: If you freeze all the layers but the last 5 ones, you only need to backpropagate the gradient and update the weights of the last 5 layers. In contrast to backpropagating and updating the weights all the layers of the network, this means a huge decrease in computation time. For this reason, if you unfreeze all the network, this will allow you to see the data fewer epochs than if you were to update only the last layers weights'.
Accuracy: Of course, by not updating the weights of most of the network your are only optimizing in a subset of the feature space. If your dataset is similar to any subset of the imagenet dataset, this should not matter a lot, but, if it is very different from imagenet, then freezing will mean a decrease in accuracy. If you have enough computation time, unfreezing everything will allow you to optimize in the whole feature space, allowing you to find better optima. 


To wrap up, I think that the main point is to check if your images are comparable to the ones in imagenet. In this case, I would not unfreeze many layers. Otherwise, unfreeze everything but get ready to wait for a long training time.