Enemy gunfire is particularly deadly in this installment. If you're not putting cover between you and the Peggies, you're going to have some trouble. One of the solutions I've found is to trade your assault rifle for an M60 as soon as possible. A center-mass burst of 7.62 NATO seems to work pretty reliably at dropping cultists quickly, which can be important in missions where you're getting swarmed.
As for the previous games: Far Cry 1 is completely unrelated. It's not an open-world game, instead presenting you with a linear progression of (admittedly large) levels. It's also more fantastic than the rest of the series, with mutant monsters running about the place, and can be frustratingly difficult at times. Far Cry 2 is a drab, dreary semi-open-world game set in Africa. I got about halfway and stopped playing because it was such a damn slog. It also featured that most heinous of game mechanics: weapon degradation. The better the gun, the faster it rusted into uselessness, to the point where sometimes a given weapon wouldn't survive a single firefight. (It also got a sponsorship deal from Jeep, so get ready to see dozens of pristine Wranglers in darkest Africa.) Far Cry 3 was the first of the current "style" of play, with a fully-open world, crazed wildlife, and over-the-top villains. I quite enjoyed it, to the point of reaching 100% completion, something I very rarely do. Far Cry 4 is generally considered to be more of Far Cry 3. Far Cry 5 has made some changes, like having exploration be more organic - i.e., in 3 and 4 you unlock the map by climbing radio towers, little platforming challenges that way outstay their welcomes, whereas in 5 you discover things by simply driving around and talking to people.