What exactly do you see on the signal indicator on your iPhone 5 when you try to connect to the internet?
If you see LTE, 4G or H+ as the indicator, you should notice a significant increase in the speed of browsing. Based on my experience, only when H and E appear would I experience poor internet connection. H (HSDPA) and E (EDGE) are the lower bands of signal transmitted by Globe towers.
If you are in a location where 4G LTE or 4G HSDPA Plus is available, your browsing should be smooth and trouble-free.