Monteverde is a lot different than the rainforests around Manuel Antonio because it is cloud forest- it’s much cooler and misty, with slightly different plants and animals. But with only 5 days in Costa Rica, your best bet is to just go to Manuel Antonio and do day trips out of there. The roads around Monteverde are rough and you would be spending a lot of time in the car trying to fit in both places.
I can’t think of any hanging bridge facilities near MA other than Rainmaker Park, but their bridge system is pretty extensive. It’s definitely rustic, but the surroundings are beautiful. You can learn more by reading our post about it: https://www.twoweeksincostarica.com/rainmaker-conservation-project/.
We really enjoyed Carara National Park. It has a small, but nice, trail system. We saw monkeys and tons of birds (it’s a must if you’re into birding, especially the Meandrica trail).
You might also want to check out some of the sights to the south of Manuel Antonio in the Uvita/Dominical area. There’s a really nice waterfall and some good places to hike. This blog post has more info: http://www.twoweeksincostarica.com/the-costa-ballena-uvita-dominical-and-ojochal/.
Hope that helps. Let us know if you have any more questions.