The Raynox DCR-250 is not a lens, per se... it's an auxiliary lens or a conversion lens. It attaches to the front of another lens to increase that lens' magnification. Image quality greatly depends upon the lens the DCR-250 is used with. Any shortcomings of the lens will be magnified by the auxiliary. There will also be variation in how high magnification will be possible, depending upon the max possible mag of the lens the DCR-250 is paired up with. The auxiliary lens simply magnifies that by 2.5X (there's also a milder DCR-150 that gives 1.5X mag).
You'll also be somewhat limited to using the DCR-250 with lenses that have small diameter front element. The DCR-250 uses some sort of "snap on" mounting so it can be fitted to lenses with filter threads between 52mm and 67mm. However, the actual diameter of the DCR-250's optics is something less than 43mm (the thread size on the rear of it). As a result, there will be significant vignetting with many lenses. In other words, only part of the image area will be usable because the DCR-250's mounting frame is blocking the periphery. This essentially reduces the resolution of your images, since much of the camera's sensor is blocked. How much vignetting occurs will vary depending upon the lens the DCR-250 is used upon.
If you want to shoot close-ups on a tight budget, instead of either of the Raynox conversion lenses, I'd recommend "macro extension tubes". Those fit in between any of your current lenses and the camera body to make the lens focus closer. These are much more "universal", able to be used with a greater variety of lenses than an optical magnifying auxiliary lens. There are various tubes available.... I recommend the Kenko set of three that sells for about $130. Those are top quality and include 12mm, 20mm and 36mm tubes, which can be used individually or in combination with each other. There are also cheaper, more plasticky sets such as the Vello for $80, which includes three tubes in the same sizes as the Kenko.
All these tube sets have electronic connectivity, so that modern lenses used on them will be able to autofocus and so that the lens aperture can be set. There are even cheaper (often under $25) sets that DO NOT have that connectivity, so are next to impossible to use with modern lenses (they work fine with vintage, manual focus lenses that have a built in aperture control ring).
Image quality with a Micro-Nikkor 105mm f/2.8 AI-S will likely be much better and a true macro lens is faster to work with than auxiliary lenses or extension tubes.
Are you looking at new or used? New the 105mm AI-S sells for $800 (or, gray market/no warranty: $730). Factory refurbished are available for $540. This is the manual focus only lens that's been in production for many years... at least since the 1990s and film cameras. It's fine, but it's also a 1:2 lens, which some people will argue means it's not "true macro". Some folks think a lens has to be able to produce full 1:1 or life size images to be considered macro and that half life size such as the AI-S lens produces falls a bit short. In truth, there is no clear definition of "macro" and a lot of "macro" shooting is half life size or less... call it "close-up" instead of macro, if you wish. Plus, extension tubes can be used with the 105mm AI-S to push magnification higher, if wanted.
HOWEVER, if you're looking at spending $800, for that kind of money you might as well get the modern AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens instead. It only costs $6 more than the manual focus AI-S lens! The AF-S 105mm is the modern version that will autofocus on your D5100 and it can natively render full 1:1 magnification. For use on a modern Nikon DSLR, it makes a lot more sense to buy the modern AF-S lens than the vintage AI-S lens! But if you are buying used and have found a good deal on an old 105mm AI-S, that can work well, with some limitations (manual focus only, 1:2 only). I found some used/refurbished AF-S 105mm for $600-650. You might do a little better with some careful searching and shopping, but it's a very popular lens and doesn't get heavily discounted.
There are some good, lower cost alternatives....
Someone suggested the Tokina AT-X Pro 100mm f/2.8 macro lens as an affordable alternative on sale for $349. It's certainly is a possibility, but you need to be aware it will be manual focus only on a D5100 (or any other D3000 or D5000-series Nikon). This isn't necessarily a deal killer, since a lot of macro shooting is more easily done with manual focus techniques anyway. It might be more of a consideration if you plan to use the lens for non-macro purposes. The reason it's manual focus only is that it's what's sometimes called a "D-type" lens in Nikon mount... the lens itself doesn't have a focusing motor. To autofocus, it relies upon a motor built into the camera body. But only Nikon D7000-series and higher models have that. Your D5100 doesn't. Nikon themselves still makes some lenses that don't have a built-in focusing motor (the Micro-Nikkor 200mm f/4 is an example).
You also might want to consider the Sigma 105mm f/2.8 EX DG OS HSM macro, which is on sale currently for $469. This lens will both autofocus on your camera and it can do full 1:1 magnification. It also features faster "ultrasonic" type focusing motor (same as the AF-S 105mm) and it has OS image stabilization (similar to the VR on the Nikkor AF-S 105mm).
I'd also suggest the Tamron SP 90mm macro lenses. There are two models of those now being offered, both capable of full 1:1 and both able to autofocus on your camera. The cheaper ($449) one uses slower/noisier micro motor focus drive and doesn't have image stabilization (Tamron calls that "VC"). The more expensive one ($649) uses a faster ultrasonic focus motor and has VC.
The more expensive Tamron is also an "internal focusing" or "IF" lens. This means it doesn't increase in length as it's focused closer. Some macro lenses nearly double in length when focused to their maximum magnification, reducing the "working distance" between the front of the lens and your subject. The less expensive Tamron 90mm and the Tokina 100mm both are NOT IF lenses. Both the Sigma 105mm and the AF-S 105mm Nikkor ARE IF lenses.
There are some other macro lenses available, but the above are probably some of the most popular for use on Nikon cameras. A lens with 90mm, 100mm or 105mm focal length is a good choice, too, because it is a reasonable compromise for general purpose, hand held shooting out in the field.
The Raynox DCR-250 is not a lens, per se... it's a... (
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