China has a carrier. China is in the process of constructing their second carrier. The US Navy recently sent officers to see the ship and discuss carrier operations with the Chinese.
http://swampland.time.com/2014/01/20/china-doubling-its-aircraft-carrier-fleet/
We cannot crank out multiple carriers per year. The GERALD FORD has been under construction since 2005. It is due to commission later this year. The legacy Nimitz-class aircraft carriers take, on average, five years to build. Right now, we can't get carriers out of overhaul (major maintenance periods) in less than eight months, let alone building a brand new one. We have no other designs to "churn out" at this point.
Naval power is not determined by the presence or absence of aircraft carriers. China's ability to cover everything west of the Marianas with a combination of shipboard, submarine, and coastal anti-ship cruise missiles will make it very difficult and dangerous for the United States to create a CVN presence in the SCS in the event of a shooting war. In fact, it is unlikely the US would be able to get a CVN within range of mainland China or Taiwan in the event of conflict in SCS or Taiwan.
China possesses the ability to track our emissions anywhere in the world. This renders the Aegis weapons system we rely on to protect the CVN mostly useless, and as mentioned above, their capacity to saturate our defenses - if we're able to turn them on in the first place - by striking from 360 is something we can't combat right now.
China possesses skywave radar technology which allows them early warning of any aircraft, as well as the ability to detect aircraft operations, as far out as the international dateline. That means any aircraft launched from Guam, Japan, or "any of those little islands nobody knows about" (except me because I've been to a lot of those little islands nobody knows about) will be detected and able to be countered long before it becomes a threat.
China's ability to out-gun our surface combatants in a shooting war is well-known. Our ASCM (anti-ship cruise missile) capability has remained stagnant since the 1980s. The HARPOON missile, while reliable, possesses a range in the 80nm window. Meanwhile, China possesses a number of active and semi-active missiles with ranges out to 400 miles. Some of those weapons can be fired from diesel submarines, which are incredibly difficult to locate because they spend the majority of their combat time operating on battery which makes them exceedingly difficult to detect except for the couple of hours every four days they come to the surface to change out their air.
That means our destroyers and cruisers are inside the missile envelope of Chinese destroyers, frigates, cruisers, and submarines from the time they are in the vicinity of the Phillippines, and are currently unable to fight back due to being out-ranged by their missiles.
This doesn't mention that nearly every one of China's high-end missiles are designed specifically to defeat Aegis as well as the Phalanx CIWS through both flight profile, high-G terminal maneuvers, and saturation doctrine. Our ships are plenty capable of defending themselves with soft-kill against one or two missiles, but against stream raids the Navy has long relied on Aegis doctrine to combat the missiles, but the missiles currently being fielded are designed to defeat that system by delaying detection range to the until they are already terminal, at which point it's highly likely that you will achieve enough leakers to destroy ships before they even get to the fight.
Our best bet for combatting all of this is our current submarine force. Go look at those numbers. Divide them in two for how many we have available at any given time. Then divide that number in two for the fact that we have two coasts splitting those resources. Essentially, we have an advantage under the surface of the ocean in terms of proficiency and technology, but they've got 10 submarines that operate in that water 100% of the time for every one of ours.
The Navy is working on various solutions to solve this problem, including upgrading the ASCM capability on our surface ships, including LCS, as well as re-invigorating the anti-ship Tomahawk program that was scrapped in the 1990s.
You mentioned five carriers active at any given time.
If China moves on Taiwan or the SCS, the US has one CVBG immediately available, that which is forward-deployed in Japan. There are presently five carriers stationed in the Pacific Fleet AOR. At any given time, up to three of those are deployable, so instead of five carriers, you're going to have one that can respond immediately, with perhaps two more available after the first few weeks of the conflict. As mentioned, once they are there, we are likely unable to establish any kind of air superiority in the area due to China's ability to deny access to the areas where the fight would be.
No one of any sense has considered carrier-vs.-carrier battle as the gold standard for Naval warfare since 1945. The CVN is there to provide presence and establish air superiority. The Carrier BG as a rule has operated in a permissive environment since WWII, and our Navy has not had to fight a near-peer competitor in more than 60 years for dominance in the air or on the sea. In that regard, our warfighting leadership is every bit as inexperienced as the Chinese.
Now, this isn't to paint the Chinese as 10-feet-tall. They're not. But many people would tell you that their Navy is near-peer, and certainly not 30 years behind ours. They have this fight in their backyard, and they have the ability to push us out of that backyard and right now there's not much we can do about it.
Now, ask me how I know all that.
You're way out of your element, quoting capabilities and making assumptions based on information you learned in world history class about how the Navy worked 80 years ago. Like Donald Trump, you don't even have a basic understanding of anything the Navy does, from operations to technology to procurement. It's Reason Number One why he has no business whatsoever being President of the United States. He thinks we're holding all of the cards at every table in the world.
We're not.