Does it make sense to user Standard Scaler after applying Label Encoder?
If you use LabelEncoder for a category, you need to make sure that your category can be comparable. For example, for category ['high', 'med', 'low'], items are comparable, so it makes sense to LabelEncoding it and standard scaling it.
However, when your category cannot be compared to each other, label encoding it would not make any sense. For example, you cannot compare 'Monday' to 'Tuesday'.
TL;DR 
If your category is comparable (ordinal), it makes sense. If not, try to find ways to reduce your category, there are a lot of methods to do so.
I'm starting a project on a dataset that contains over 5k unique values for a category.  
My question is, after using label encoder, to "enumerate" the categories, does it make sense to use Standard Scaler to make the data a little more "manageable" for my Machine Learning model?  
Keep in mind I have over 500k entries in total and 5k unique categories for this particular column.
This is more about the intuition behind it rather than how to code it, but I figured this should be the place to ask.