How do I filter outliers in test data based on z-scores of train data?

Question

I have a train and test dataset. On the train dataset I detected and deleted outlier values, when their standard deviation is 5 times greater from the mean. If a z-score returned is larger than that, the value is quite unusual and therefore I delete it from the dataset.

import scipy.stats as stats
z_scores = train_df.apply(stats.zscore)

abs_z_scores = np.abs(z_scores) 
filtered_entries = (abs_z_scores < 5).all(axis=1)  
train_df= train_df[filtered_entries] 

Now I want to use the same z-scores based on the train set to remove values from the test set. (I don't want to get the z_scores from the test dataset itself!) Probably one idea is to store the mean and standard deviation of X from the train data and calculate the z-score for the test data based on them e.g.

(Xtest−μ)/σ

But I do not have any concrete ideas how to do so. Could someone give me some advice?