The GTX760 will work perfectly with your current motherboard.
Make sure the new power supply has at least two 6 pin PCI-E leads to power the new card.
Check the card will fi in the current case! Get out a tape measure and check.
It is unlikely the existing CPU will bottleneck a GTX760 but you should look into overclocking it, those old i5 chips overclock very well although I doubt the Gateway motherboard will allow such games.
English is my first language and I STILL make mistakes in it.