I'm no expert, if your Beautiful dog doesn't want in right away, he must want more time outside. I know dogs that love being outside, but you have to be careful so they don't get too cold.
You mentioned walking him, maybe he wants to run?
Is your walks 1/2 hour at a time or longer? Puppies need a lot of exercise.If you can go 3-4 times a day for a few days to see if that makes a difference.If he was forced to stay in the house day and night with the previous owner he may just want to be outside for awhile. Make him stay inside at night anyway.You are the "pack" leader.We have coyotes here that have killed 4 cats in the neighborhood since last summer. Make sure he can't get out of the yard. DH takes Buddy out 5-6 times a day. Here is Buddy after a long morning walk.
Good Luck GGVi
Congrats on the dog. Walking twice a day is great; just make sure they're long (30-40 min) walks that are brisk enough for you to break a sweat and get your heart rate up. Dogs do not get exercise sitting in a yard by themselves.
Simply bring the dog inside as the other writer suggested. After only 5 days the new home is still a little different from his previous home. Dogs should NOT be kept "outside" by themselves at any time.
They will annoy neighbors before you hear them and they are prime targets for dog-nappers.
No, that's not a joke. More dogs are stolen than ever run away from boredom.
Make coming inside a fun training exercise and use good treats. You need to let the dog know what is expected of them or they will try to figure it out on their own. When they make the decisions; it's unlikely they will behave as you would prefer. It also leaves the dog mentally under stimulated which will bring on behaviour problems.
Give the dog a definite bed and train him to use it through treats and praise. He'll get the idea very quickly.
Congratulations on your new dog. My son has an American BullDog; a very loving and loyal dog but not the smartest dog I've ever known--this is not a bad thing, however. If you want the dog in, bring him in. If it doesn't matter then let the dog stay out. You are the leader, you decide what the procedure will be. At 5 months the dog is still very immature and has a lot to learn. He has a strong desire to please you so take advantage of that.
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