I was not sure if I should answer this because as anongoodnurse pointed out, this sounds like a complicated situation with many possible interpretations, even for professionals who are on site. Obviously a lot is going on around this kid, so the first thing is really to decide if this is more than childhood tantrums, emotional transitions etc etc. As your gf has contacted the psychiatrist, I am guessing her parenting instincts tell her that yes, this is something more and she needs help with this.
I decided to bite the bullet to put down some links on childhood depression:
Lifted from the link: most kids with significant depression will suffer a noticeable change in social activities, loss of interest in school and poor academic performance, or a change in appearance.
I want to emphasize that depression can show up differently in children and adults. https://www.mindwell.us/differences-childhood-adult-depression/
A loss of interest in things that they usually take pleasure in is also a red flag in children.
Because this has been going on from 4-7, it will be helpful if she can recall earlier events to see if there was a transition point and possible trigger events. This history will also be useful to any professional who sees him subsequently.
Bear in mind that depression usually signals something deeper. When that something deeper is identified and addressed, the child will get better.
On professionals, I am surprised that she contacted psychiatrists rather than psychologists or even counsellors. Is there a particular reason why? They are related but they do different work. A psychiatrist can rule out that his behavior does not stem from biological causes (e.g. chemical imbalance). He cannot offer much help beyond that partly because of the child's young age. A psychologist cannot test for chemical imbalance, but he can do personality profiling, socio-emotional developmental profiling, and locate any missing or delayed areas. A competent one should also provide you with tools and strategies to help the child develop in those areas, or refer the child on for further help(eg with occupational therapist, audiologist) as he thinks may require.
Here is more on their differences: http://www.webmd.com/mental-health/features/psychologist-or-psychiatrist-which-for-you#1
I will also very much encourage approaching the school counsellors and any other trusted adults for assistance. There can be things going on in school that we at home cannot be aware of. It can be social issues, or it can be undiagnosed learning disabilities that show up most in school if you are not actively coaching the child. Both of these can wear a child down and make him feel like a failure every day, over and over again. He may also feel more able to open up to another adult when discussing his feelings towards school and home.
If the situation is revolving mainly around home, I will consider if he is being treated like the runt of 4 brothers among other things. It will be good to put aside 2 time slots a week: a 1-1 with him (appreciation time), and a family activity to improve bonding. If weekly is too difficult to achieve, try every two weeks instead. To squeeze the maximum returns out of this time, consider using tips from the 5 Love Languages of Children. https://www.amazon.com/5-Love-Languages-Children/dp/0802403476.
Regarding discipline, given that he is already very negative, try to gear towards positive reinforcement, setting achievable targets in tandem with teaching him strategies to cope with negative emotions. E.g deep breathing to calm down, go for a walk, go to his peaceful corner (you have to make one for that) etc. So if he manages to moderate a meltdown halfway and walks off to his peaceful corner and starts howling there, that is progress. (1 sticker) I may also be more old-fashioned in the sense that I will require the older children to hold back during a provocation and give me the space to deal with this instead of adding oil to fire. This does not mean condoning his behavior, but it means keeping a lid on the situation. Mum can make it clear that she appreciates their help with this.(1 sticker) Put up individual reward chart and family reward chart. Stickers go on individual AND family chart and the family bonding outing can be the reward for all their combined "goodness" (patience, understanding, self-control).
All the best!