A swiping keyboard requires capacitive touch. Capacitive touch requires more energy than just a hardware keyboard. There are Android phones without touch capabilities and only hardware keyboards, especially in developing countries, but I do not think that's what you want. Also, those phones do get security updates, but they will never go above Android 2.3x because they only have a single core processor.
An FM radio requires a wired earbuds/headset to act as an FM antenna. Phones in developing countries have that functionality enabled as well, since data connections can be very expensive otherwise. Camera, don't aim higher than 2MP or 3MP, if you want something better, you'll need to carry an extra standalone camera with you (or actually buy a better phone). Podcast playback implies longer battery usage. You'll be able to do it, but you shouldn't do it if you really want to conserve battery power.
You'll also need to keep your data turned off, buy yourself an extended battery with good reviews, and live near a cell phone tower if you want to get yourself closer to your goal of multiple days without a single charge. By the way 5 days may be pushing it, if your battery is the size of a briefcase, like in the olden days of early cell phones, then may be you have a shot at lasting 5 days, but then you'll have to carry a very heavy briefcase everywhere you go. Also, I mentioned that you needed to be near a cell tower, because if you live near a cell tower, your phone doesn't keep retrying the connection every few seconds, your phone wastes less battery energy, and your phone actually irradiates you less.