when will the accuracy of binary classification on mnist 1 and 5 get better?

Your y_train and y_test is filled with class labels 1 and 5, but sigmoid activation in your last layer is squashing output between 0 and 1.

if you change 5 into 0 in your y you will get a really high accuracy:

y_train = np.where(y_train == 5, 0, y_train)
y_test = np.where(y_test == 5, 0, y_test)

result:

64/64 - 0s - loss: 0.0087 - accuracy: 0.9990

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