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The following sutta quote shows that it can be in any order. There's no automatic cleansing of past bad deeds after taking triple refuge and the vow of the precepts.
"Now, Ānanda, in the case of the person who takes life... & holds wrong view and, with the breakup of the body, after death, reappears in a plane of deprivation, a bad destination, a lower realm, hell: Either earlier he performed evil action that is to be felt as painful, or later he performed evil action that is to be felt as painful, or at the time of death he adopted & carried out wrong view. Because of that, with the breakup of the body, after death, he reappears in a plane of deprivation, a bad destination, a lower realm, hell. And as for the results of taking life... holding wrong view, he will feel them either right here & now, or in the next [lifetime], or following that.
"In the case of the person who takes life... & holds wrong view [yet], with the breakup of the body, after death, reappears in a good destination, a heavenly world: Either earlier he performed fine action that is to be felt as pleasant, or later he performed fine action that is to be felt as pleasant, or at the time of death he adopted & carried out right view. Because of that, with the breakup of the body, after death, he reappears in a good destination, a heavenly world. But as for the results of taking life... holding wrong view, he will feel them either right here & now, or in the next [lifetime], or following that.
"In the case of the person who abstains from taking life... & holds right view and, with the breakup of the body, after death, reappears in a good destination, a heavenly world: either earlier he performed fine action that is to be felt as pleasant, or later he performed fine action that is to be felt as pleasant, or at the time of death he adopted & carried out right view. Because of that, with the breakup of the body, after death, he reappears in a good destination, a heavenly world. And as for the results of abstaining from taking life... holding right view, he will feel them either right here & now, or in the next [lifetime], or following that."
"In the case of the person who abstains from taking life... & holds right view [yet] with the breakup of the body, after death, reappears in a plane of deprivation, a bad destination, a lower realm, hell: Either earlier he performed evil action that is to be felt as painful, or later he performed evil action that is to be felt as painful, or at the time of death he adopted & carried out wrong view. Because of that, with the breakup of the body, after death, he reappears in a plane of deprivation, a bad destination, a lower realm, hell. But as for the results of abstaining from taking life... holding right view, he will feel them either right here & now, or in the next [lifetime], or following that.
MN 136
However, the suttas do speak of stream entry as the point after which one definitely does not go to lower worlds.
Someone who understands and sees these principles is called a stream-enterer, not liable to be reborn in the underworld, bound for awakening.”
SN 25.1
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Based on the Dharma Sermons I've listened so far. Obedience to 5 Precepts does not guarantee that person won't be born in one of the 4 Hells. It also doesn't guarantee the next life as a Human, Deva or Brahma too.
Attaining Sowan (Sotapanna) — 1st stage of awakening — by listening to Niravana Dhamma is THE only minimum guaranteed way to stop being born in one of the 4 Hells.
Because that's when you have beat the biggest Misdeed — Pure Delusion.
There are cases where people have been born in hell after obeying 5 precepts their whole life. As well as people who were born as Deva, Human even after doing many misdeeds.
Anyone below the Sowan Stage has a huge potential to be born in Hell even if they do good things as considered by the society. There is a lot to understand before realizing how a person go to hell, how a human life is formed etc. But all that is available in Tripitakaya.
Converting to Buddhism and following Buddhist Practices as a lay follower will cleanse your Bad Karma, Misdeeds by the amount you follow these things. However, you can't neutralize all your Karma, Misdeeds without attaining Arahat stage.
It doesn't matter if you killed people in the past, just following 5 precepts won't save you from Hell. Attaining Sowan stage is the only guaranteed way.
Angulimala is a person who killed so many people before attaining Arahat stage. He didn't go to hell with all those murders. He achieved Nibbana at the end.
If you have done bad stuff in the past, acknowledge that. Then focus on following Buddhist practices such as Daily Gatha, Pirith, Sutra Chanting. Listening to Nirvana Dhamma and Meditation to make your life better. This will save you from a ton of suffering. Not just this life. BUT every life that comes next.
That's the power of Buddha Dharma. You'll gain the good benefits until you attain Nibbana one day! Hope this answer helps you.