You have not missed any options for CS5 opening the raw data, directly. The D7100 requires at least CS6/ACR 7.4 or DNGC 7.4 that will make DNGs that will open in older ACR versions.
DNGs may different in size from the NEFs due to differences in lossless compression or a different-sized embedded preview image or even missing Nikon-only metadata in the DNG. In other words, the photosite values for the sensor data should be preserved but the packaging of, or the other data around, the sensor data may be different.
The cheapest option to make PS work with the native raw files is likely PS-CC for $10/month as part of the Photography Plan.
Another option is to purchase (serial number version) or rent (CC Photography Plan version) Lightroom and use it to do what you’d normally do in Bridge and ACR, and then use Edit In Photoshop w/in LR to do finishing touches in your older PS. This option renders a TIF or PSD to disk with all your raw-file adjustments and then passes this file to PS for further editing. The one caveat with buying the serial-number LR is that a new version of LR is probably about ready to come out and waiting until that new version is available would save money.
One thing to consider is that the PS-CS6/ACR 7.x has a new toning model which is an improvement for most images and you don’t have access to that if you’re not using at least CS6.
The reason Adobe doesn’t add new camera support to CS5 (and CS4 and CS3 and CS2 and CS and 7, 6, 5, 4, 3, 2, 1) forever is because they want to be paid for their work, and if every camera update was free forever people would only buy PS, once, and would keep using that without paying anything more until maybe the OS on their computer wasn’t compatible, anymore. This is one reason Adobe went with CC, so people would pay a little continuously and this constant cashflow would better match Adobe paying their employees continuously, instead of having to budget for the future based on how many new customers might buy an upgrade every 1.5 years or so.