In Grand Theft Auto 5. can you go inside your house after buying it?
In story mode you can. Though you can only go inside the house they have given you and you can't buy any other house in story mode.
But in the online mode you can buy any house, and go inside of it.
So, that means you can go inside whether playing online or story mode.
Here is the waypoint of the house..
You can go inside by walking onto the blue marker. It has some things inside, like a bed, a shower, and other things depending on the property you bought. You can make your character spawn there whenever you join Online by going into the Interaction Menu (M on PC, Back on Xbox, Select on PlayStation) and scrolling down to "Spawn Location". You can change that to your property.
All 3 characters have thier own houses in story and they are all enterable. However you cannot buy houses in single player so do you mean online?
If you are talking about online then you can go inside your house once you buy it. You can take a shower, lie on the bed, drink the drinks that are there, sit down and watch TV. You can set it as your spawn location too.