Is observing the five precepts a gradual training?

Question

Which Pali suttas refer the subject of "gradual training"?

Do the Pali suttas say observing the five precepts is a "gradual training"?

Answer 1

While the five precepts are not a form of gradual training (since it is the minimum prescribed practice), the Noble Eightfold Path is certainly a gradual training as evidenced by the following quotes:

From Ud 5.5:

Just as the ocean has a gradual shelf, a gradual slope, a gradual inclination, with a sudden drop-off only after a long stretch; in the same way this Dhamma & Vinaya has a gradual training, a gradual performance, a gradual practice, with a penetration to gnosis only after a long stretch. The fact that this Dhamma & Vinaya has a gradual training, a gradual performance, a gradual practice, with a penetration to gnosis only after a long stretch: This is the first amazing & astounding quality of this Dhamma & Vinaya because of which, as they see it again & again, the monks take great joy in this Dhamma & Vinaya.

From MN 70:

"Monks, I do not say that the attainment of gnosis is all at once. Rather, the attainment of gnosis is after gradual training, gradual action, gradual practice. And how is there the attainment of gnosis after gradual training, gradual action, gradual practice? There is the case where, when conviction has arisen, one visits [a teacher]. Having visited, one grows close. Having grown close, one lends ear. Having lent ear, one hears the Dhamma. Having heard the Dhamma, one remembers it. Remembering, one penetrates the meaning of the teachings. Penetrating the meaning, one comes to an agreement through pondering the teachings. There being an agreement through pondering the teachings, desire arises. When desire has arisen, one is willing. When one is willing, one contemplates. Having contemplated, one makes an exertion. Having made an exertion, one realizes with the body the ultimate truth and, having penetrated it with discernment, sees it.

Answer 2

Blockquote"It is possible, brahman, to lay down a gradual training, a gradual doing, a gradual practice in respect of this dhamma and discipline, Brahman, even a skilled trainer of horses, having taken on a beautiful thoroughbred first of all gets it used to the training in respect of wearing the bit. Then he gets it used to further training — even so brahman, the Tathagata, having taken on a man to be tamed, first of all disciplines him thus:

https://www.accesstoinsight.org/tipitaka/mn/mn.107.horn.html

You can start observing with one precept first. For instance, you can stop consuming alcohol forever even though you still may be breaking the other four precepts or you can stop killing humans but you may still kill animals. You know breaking five precepts is unwholesome but you still may break them. Knowingly breaking five precepts is better than doing it unknowingly. This is not ideal but you have to start it somewhere.