New panda strike & Multiple pages about the same keyword

4-5% keyword density, are they even readable? Definitely need to reduce it.

this is proof that social signal will play more and more important role in SERP

You should reduce your Keyword density into 1-0.6. You can basically remove the rest of other keywords or you can mix up your anchor text. Google update says that partial match anchor is better than full exact match.

Stuffing your pages with keywords will get you exactly what your getting now, poor SERP results.

If your considering removing the pages, that tells me those pages must be very poor quality content. Nobody removes pages that they are proud of.

I hate panda

What you should do is a variation of #1. First things first, the most important thing is giving your website an architecture that makes sense. For example:

Main Theme: Weight Loss
Child Theme: Cardio Work Outs
Grandchild Theme: Riding Your Bike

If your site has an overall theme of weight loss, you should make child themes of different types of weight lifting, cardio, nutrition, etc. From there you want to break your main theme into child themes and grandchild themes. Once you've established website architecture that heavily themes your site into appropriate nesting categories, you can begin to work out what content is worthy.

So let's assume you've written 10 articles loosely based on riding a bike. You've got one article about riding a stationary bike at home, another on stationary bikes at the gym, another on different types of bikes, another on what to do while riding the bike (reading a book, listening to music etc). Now previously all of these articles were ranking but they all had the keyword focus on "riding a bike". What you should do is map out all of the content that can be found within these articles and decide whether or not they deserve their own article, or if they can be combined into one article. If you have a lot of fluff spread over 10 articles, then combine them into one big article. If there's a lot of meat or you could go back and rework all of your articles so that they had a lot of meat, then continue breaking down your site structure like this:

Weight Loss
-Cardio
--Riding A Bike
---Stationary Bikes
---Bicycle Work Outs

Then from there add your articles under their proper parent theme:

Weight Loss
-Cardio
--Riding A Bike
---Stationary Bikes
----Things to do while riding a stationary bike
---Bicycle Work Outs
----Mountain bike or speed bike for daily riding?

If an article serves the exact same purpose as another article on your page, then you should combine the two articles putting the meat of both them onto on page. If they both serve their own purpose, then structure them somewhere within your website architecture that they serve their own clear purpose while rewriting them so that they're not targeting the same keyword.

I run a site on Presidents, they did an update like this with one of the earlier Pandas so I merged my pages (President Name Facts, President Name Biography, President Name Quotes) into just one page per president using tabs. This recovered the rankings until today. Today they have again lost their rankings. Not sure if this is a new panda or because I changed my DNS to cloudflare.

Anyway my general advice is don't over create pages - make longer ones as you'll get a hell of a lot of long tail visits that way as each page has more authority and direct back links to it.

Too many keywords are always penalised, event before panda etc