Hi there! First off I'll apologise if I touch on anything you already know all about, but you said in 'plain English' so I'm going to write the following with the assumption that you don't know it already
Red streaks in the tail or fins is generally an idicator of septicemia (blood poisoning). This can be caused by several different things such as an infected injury to the affected area (perhaps the tail was scraped on an ornament or something and the wound became infected), a secondary infection caused by finrot or poor water quality. Once the infection reaches the base of the tail and starts to progress up the body then it can be very difficult to treat.
You said that you recently set up the new 5ft tank and added four more goldfish all at once after adding the original pair. Aquariums can take a few weeks to cycle when they are set up ('cycling' is the term applied to the maturation of the bacterial colonies in the tank... here are some pages about cycling:
http/www.thetropicaltank.co.uk/cycling.htm http/www.thetropicaltank.co.uk/cycling2.htm ). The bacteria that needs to become established in the tank helps to break down the fish waste and turn the ammonia (harmful to fish) that the fish produce into nitrites (slightly less toxic but still harmful), which is then broken down by different bacteria which then produce nitrates (relatively harmless, but can cause lots of algae to grow). Because it takes a bit of time for the bacteria to colonise in the water, the filter sponge and the sand/gravel (especially in a tank that's as big as a 5ft one) the water becomes full of a backlog of ammonia and nitrites because there isn't enough bacteria in the tank to consume it. Basically the ammonia and nitrites then begin to poison the fish causing different illnesses. The fact that you added four more goldfish so quickly after setting up the tank will be adding more fish waste than the bacteria could handle at that point.
I would begin by increasing the amount of water changes you perform. Remove and replace about 25% of the tank water every other day. This will help to remove and dilute the pollution in the water. Also, you don't need to feed your goldfish every single day... one good feed every other day is fine. Excess food in the water will add to the ammonia buildup and the more your fish eat the more they will excrete! Obviously I'm not saying starve your fish, but once every other day is fine. If you know other people with fish tanks that have been set up for quite a long time you could ask them for some of the sponge from their filter and some tank water (provided that non of their fish has any illnesses and everything is nice and healthy) to help add good bacteria to your own tank and help things along slightly.
The trouble with septicemia is that you will need to introduce an antibiotic to the water to try and combat the infection. However, this can also sometimes weaken the good bacteria in the tank! However, I would still recommend that you treat with an antibiotic as it sounds as though the infection is quite advanced since the fish are listless and the red discolouration is visible on the body at the base of the fins. Waterlife's 'Myxazin' is designed to help combat finrot and infections. Look here:
http/www.aquatics-online.co.uk/Z121256.asp
I really hope things start to look up for your two ill goldfish, but it sounds like the infection is quite bad