DSL v5 is a fitting formula that determines how much gain and compression is considered “best” for you specific loss. I think it is a very important issue, and potentially the most important aspect that determines how a hearing aid will sound to you. Many hearing aid users focus on the brand and model of hearing aid, and the latest bells and whistles that they have. My conclusion in being new to this, and learning, is that the fitting formula is much more important than the brand and model.
When you shop for hearing aids the fitter will let you try different aids, but probably does not tell you what fitting formula is being used to program the hearing aids. It can be the proprietary formula from the manufacturer, or it can be an industry standard formula like NAL-NL2 (Australian), or DSL v5 (Canadian). They will all sound different. However, it is hard to tell you in advance which will sound best to you. That is why I recommend at very minimum finding out what formula they are using, and to what experience level it is being set at. And if possible trying different formulas to see which sounds the best to you.
Here is the DSL v5 formula which I posted earlier. It shows how much gain is applied to soft (top light line), normal (middle heavy line), and loud sounds (lower light line), across the frequency range.
This is the NAL-NL2 formula applied to your loss. The wider separation between the lines means that more compression is being applied. Loud sounds are amplified less, and soft sounds amplified more.
This is the Rexton SmartFit formula which can only be used in their aids.
So you can see there are very different approaches to how the loss is corrected.