Personally I would avoid it like the plague, full of sugar and nothing else so wouldn't waste my carbs on it.
Tesco do a no added sugar one called Mexican lime and I use this though it is a double strength so I don't use it neat in vodka as it's too strong, I usually add some diet lemonade as well. I also like a splash of it if I have the odd lager in summer.
If you are low carbing you obviously have to count your carbs and have your own limit. Some people may aim for 100 g per day so 5 isn't that much. However, some people might be aiming for only 30 per day in which case it's a major part.
These things always depend on what else you eat.
As stated, if its just the lime taste, use a sugar free verson. Personally, I use a freshly squeezed lime. The fresh juice like lemon is acid and helps reduce BG levels and the fleshy parts are high in soluble fibre and good for keeping the blood flowing.
Diet tonic water, lime, mint and elderflower makes a super drink and if you want to add vodka, it'll be better than Roses. The sweetener used in the diet tonic will stop it being too sour.