It's hard to say whether your active antenna would work properly if provided with 3.3 VDC instead of 5 VDC. I doubt that any damage would be done, but I'm not the engineer that designed the antenna. You might consider adding a boost regulator (and the other parts it requires) to your circuit, which could convert 3.3 VDC to 5 VDC. Here's such a part, selected more-or-less at random from the astonishing variety of boost regulators on offer.
Your LNA may work fine with 3.3 VDC, so you might as well just try it as-is first. A boost regulator has an inherently-noisy switching power supply inside, which might raise the noise level at the frequencies used by the GPS satellites, as @AndrejaKo points out, so there is some risk that a boost regulator would impair your circuit. However, the switching power supply internal to the boost regulator uses many of the external parts that the boost regulator requires; this gives the engineer an opportunity to reduce the noise level on the band of interest by tweaking the component values, if the noise proves to be a problem.