Were you using the highest resolution settings your camera has? (Large/Fine)

Most likely the grainyness (called noise in digital) is from using a high ISO. Using any of the pre programed modes on the camera lets the camera 'read' the light and set it's own settings based on what it 'sees' giving you no control over what it chooses. That's why those settings are called automatic settings.

In a consumer grade point & shoot digital camera the ISO at 400 is VERY grainy. If you were using a DSLR (XT, XTI etc) then ISO 400 is very acceptable even up to ISO 800. The difference is the size of the sensors in the digital cameras, a DLSR has a larger sensor, just one reason among many, they cost a bit more.

I also have the S3 (very similar to your S5) which has a supposed MP rating of 8 and my XTi has a MP rating of 10. Until I actually did some test shots I just figured the XTi was a small jump in MP, I was WAY wrong. The differences in the way the sensors do resolution is no comparison, the XTi far surpases the S3 when it comes to ISO noise. Let's put it this way a ISO of 400 on my XTi looks better than the ISO 200 on my S3.

If you do alot of sports shooting I'd recommend you use flash and a lower ISO setting. You can't do that in sports mode you'll need to use the (P) program setting so you can change your ISO yourself, you'll also need to set your own white balance too. The camera will take care of the shutter speed and aperature for you based on the lighting.

If you can't use your flash at the sporting events or you don't like the results (usually alot of flash fall off, black backgrounds, or some people overexposed while others you can barely see) then you have a few choices....

1) learn to live with the noise/grain and be happy with being able to get the pix you need, and those you posted seem fine even with the noise.

2) try one of those noise reducing programs available online for free then see if you can fix some of the noise in the pix in your computer.

3) upgrade to even the entry level DSLR's that have much better sensors and the options of later buying additional lenses that are made for low light to get even better pix.

As a general rule sports photography is one of the most expensive ones to do because of the cost of the 'faster' lenses. However as long as you are not way far from the action there is a lens available for Nikon and Canon that cost under $100 that is great for low lighting (50mm f/1.8).

BTW you can get the manual for the S5 HERE

There are two manuals, the basic and the advanced. You can download both to your computer as PDF files then you'll always have them.