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I understand the basic concepts of GPS positioning system and the use of trilateration but I don't understand why it takes so much time to get a fix.

On commercial GPS like TomTom it usually takes about one minute and on my phone it can take more than 5 minutes to be located.

Is it because of the computation time or it needs to collect more data before having a good approximation?

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The time to first fix (TTFF) is dependent on many variables such as the state of the almanac and ephemeris data on the device, the device's dilution of precision (DOP) thresholds, the current positions of satellites in the sky and any obstructions, and whether the device is using normal GPS or assisted GPS (aGPS) (which theoretically should reduce the TTFF but perhaps there are circumstances where aGPS isn't enough to make up for the quality of the device's GPS functionality).

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pocketgpsworld.com explains it quite well, might be overkill for your question on a technical level but hopefully you get a better understanding of the process to achieve a fix.

Have an old Nokia N82 (GPS receiver at the top of the phone) and will get a cold fix (no assisted GPS etc) in less than 30 secs - new models have been slower since.

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