Hello and welcome to the forum. Looking at the other way, the usual advice is just to stop the commercial food and start raw with no transition. At least that is what I was told when I put my dogs onto raw. When I took them off raw I did the same in reverse i.e. I did not transition.
If your pup is healthy and does not have a sensitive digestive system then he should be alright, particularly as he is not enjoying the raw anyway. If you want to play safe then just replace one small meal with dry food for a few days then increase it gradually so that by the end of the week he is fully on kibble. I would be inclined to give it as separate servings rather than mixing raw and kibble. I've found that this works better but that's just my experience.
As for choosing a new product, we have the Dog Food Directory
which is really useful for pet owners to source a good food. If you haven't already seen this, look for the filters on the left hand side of the page and place a tick in the boxes of your choice. As a start, you might want to try the following filters:Type of food - dry
Food properties - natural and clearly labelled
Rating - move slider to 4 to 5 stars
Avoid ingredients - all red
Click Go and it returns seven pages of products
You can narrow this down further by cost and other factors. Puppy food is usually higher in protein but a number of these products already have good protein levels so you will not find a puppy version i.e. they are all lifestage products. This is useful because you will not have to change food as pup gets older.
At five months old, pup will be changing his teeth so gums will be a bit sore. If the kibble is too hard, then soak it in warm water for about 15 to 20 minutes and it will be easier for him to eat. Also he will not be quite so thirsty.
If you locate a product that you are interested in and want to have a chat about it, please let us know and we will try to help. It would be nice to hear how you get on with pup and the new food.