We present a new method of predicting the ages of galaxies using an artificial neural network (ANN) with an evaluation of the methods such that future work can be derived for other properties of galaxies with ANNs. We train our ANN to recognise the patterns between the equivalent widths of spectral indices and the mass-weighted ages of galaxies from the Galaxy and Mass Assembly (GAMA) survey estimated by the MAGPHYS model. We quantify the quality of our predictions by calculating the mean squared error as 0.02, mean absolute error as 0.11, R-squared score as 0.53 and presenting prediction uncertainties which show our network performs well. Finally, we describe how the predictions are physically motivated as they follow trends already present in the properties and EWs of the galaxies which shows the network is able to meaningfully derive age from the EWs of galactic spectra.