Neural network for a data with 5 inputs and 1 output of 3 different types
It sounds like you want to use a regression model (which produces a real value as the output, e.g. a value in the range [-1, 1] but possibly outside as well depending on the learning algorithm) instead of a classification model (which produces one of a set of discrete output values based on the training data, e.g. {-1, 0, 1} in your case).
If the code is changed to use MLPRegressor instead of MLPClassifier, it will provide a real value as output.
Instead of:
from sklearn.neural_network import MLPClassifier
model = MLPClassifier(...)

Use:
from sklearn.neural_network import MLPRegressor
model = MLPRegressor(...)