I did the exact same thing as you, moved from an SR5 to the P5.
At first I was really not digging the bass that much at all, because I was not used to it. I had to learn to adjust my playing technique a bit because I wasn't playing next to the bridge anymore, and playing on a passive bass. I was getting a ton of clicking and clacking from my playing because of how I played on my SR5, and because of the pickup (which I'll get to later). Now I really love it, and I've gotten used to it for sure.
As for making it active, I wouldn't see the need to go that route personally. It does a great job passively for me. I considered adding a bridge pickup at one time as well, but now I don't think I need it at all, I like the simplicity and tone of the single P pickup.
I did however, do a bunch of other mods to it, which I listed in summary here:
No more Fender Precision V?. I really hated the pickup at first, until I realized that Fender never potted the pickup, which contributed a lot to the clacking and excess noise and sensitivity of the pickup. After potting it sounds great.
As for the output- Yeah, it's going to be a lot less than your SR5. You came from an active bass with a huge humbucker to a passive P bass. You most likely will have to push the amp more with the P. If you feel like you are hitting the pickup when you dig in, lower the pickup a little and cover the pole pieces in clear nail polish, it will help a lot. If it still seems too sensitive for you, pot the pickup in wax like I did and that will eliminate a lot of the popping and feedback.