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I need to use AES-128 to encrypt a plain text about 720 bits.
Is it correct to say that – in this case – the plain text will be divided in 5 blocks of 128, the result will be equal 640 bits, and the other 80 bits would be expanded to 128 bits?
The total result would be 6 cryptograms( 5 - 128 bits, 1 - 80 bits expanded to 128 bits) that will be concatenated.
In the end, what I would like to know is: what's the correct procedure to standardize the plain text to be encrypted by algorithm?
You cannot encrypt 720 bits plaintext using just AES-128. AES is a 128 bit block cipher. Such a block cipher has an input of 128 bits of plaintext and an output of 128 bits ciphertext; and that's it. You need some kind of construction to make block ciphers encrypt larger or smaller plaintext.
Such constructions are known as (block cipher) modes of operation. Some of these constructs like ECB (usually insecure) or CBC require padding (what you call "expansion"), most of the others do not. Even ECB and CBC can be used with ciphertext-stealing to avoid padding.
Probably the best way is to chose a mode of operation that doesn't require padding; CTR mode operation is probably the most used mode for new implementations. It is also the most used within authenticated modes of operation such as GCM, which come highly recommended.
If you're stuck with ECB or CBC then choosing PKCS#7 compatible padding is probably the best / most compatible padding out there. Beware of padding oracle attacks though (did I mention authenticated encryption already?).
