How terrible for you and especially your other children.
This is my unprofessional opinion; just what I would do with my child.
Firstly, your son is ill; no normal child behaves like that. He needs a checkup to see if he has Diabetes, decayed teeth, or some other chronic, irritating, complaint. I would take him to a private clinic if necessary to see a psychiatrist and to be put onto medication. It might take a while to sort out exactly what, but he needs professional help.
Secondly, the only way for you to react is to be totally consistent every time he is violent. Have an immediate ramification of his favourite toy being locked into a vault for 24 hours (and then his next favourite etc etc.) And an immediate withdrawal of your son to a secure room where he can not hurt himself nor anyone else. If out then it's straight into his car seat or a large pram with child proof seat belt. Also have an out door yard that is secure where he can be put for half an hour on his own. Always have a healthy sandwich on offer while he is calming.(He could be hangry)
He is a danger to others.
Try not to cry or react yourself; expect that he will be naughty and trust that you have a plan.
Never give into his whines for treats.
Try not to be violent in any way yourself, nor shout or become uncontrolled. (Difficult when a small boy is biting your leg off, I know.)
Once or twice per day, if you notice him being particularly kind, reward him by telling him so. Twice per week reward such behaviour with ice cream after dinner. (But withdraw the ice cream offer if he is nasty after that.)
Do you need a break by hiring a muscley man nanny for a few days every now and again, who can physically control him and activate what your words are sternly asking your kid to do. Go to the car - and strong man lifts kicking boy up and clamps him into his seatbelt. Ted is locked away for a while now go outside and play until you calm down and we call you to dinner - and strong man lifts boy outside and locks the door, and ventures out to stop boy breaking down shrubbs or breaking windows,if need be.
Set in motion a strict routine. No screens, no junk food, meal times at similar times each day and regular daily out door runs around the block, kicking balls and playing at the park. Bed times need to allow for 12 hours of sleep. Read stories and play lego and other engaging games every day for an hour with five year old. He needs boundaries, healthy snacks, active play, engaged and switched on parents as well as specialised professional care.
Predict his violence.
I would have him participate in the daily walk with you and his Dad again tomorrow but I would insist that he is strapped into a pram with secure seat belt. Tell DS5 that he was too pushy to Daddy and he is not old enought to walk safely.