From your description it sounds like the problem is in the SIM Reader Module and not the cards. If that's the case, you probably need to replace the module, which would require replacing the motherboard. There's a guide for that procedure ([guide|27075]), but you'll need to acquire a motherboard from somewhere else.
[http://www.ebay.com/itm/TESTED-ATT-Unlocked-Samsung-Galaxy-S5-S-V-5-Active-G870A-Main-Logic-Mother-Board-/331417534363?pt=LH_DefaultDomain_0&hash=item4d2a063f9b|Here's a link] on eBay that has the parts you'd need to do the replacement.
When replacing your motherboard, you should also transfer your rear and front-facing cameras from your old motherboard to your new one.
Hope this helps!