While you haven't stated whether they're interested in boarding or house sitting, it only matters a little bit but not much. Yes, you should be charging PER DOG since each dog requires your time.
From looking at your profile page here, it looks like we're talking about house sitting. What you should do is create an "additional dog" rate that would not necessarily be your posted rate for a single dog. It could be half of that amount or whatever you believe is fair. Just don't devalue yourself because bargain hunters often turn out to be the most problematic. Since you know the customer has 5 middle-sized dogs, you need to take that into account.
The additional dog rate can be found here:
https://www.rover.com/account/profile/r…
You will need to click on the + sign for them. Also, check what the prevailing "additional dog" rates are in your market (both Rover sitters and boarding facilities),.
Taking a look at your rates, I have noticed a few strange things. You are charging less on a holiday. Typically it is more. The same for puppies; they require more of your time than an adult dog. I don't know exactly how you are planning to do your house sitting (i.e., how many hours you will be at the house) but if it is for 24 hours, it seems rather low. House sitting should be viewed as a premium service because you have to uproot yourself. You aren't tied to the house but you should be spending a majority of your time there, especially in the evening through the morning.
Hope this helps!