First of all, Taraweeh is not a obligatory prayer but optional. It is a stressed Sunnah i.e. there is a great reward for those who perform it and there is no blame upon one who does not. If you want to reap great benefits, continue performing it the whole month of Ramadan. If you leave it, there is no blame upon you. Be it 5 to 10 days or even greater. But, you will be missing a great benefit.
Abu Hurairah (May Allah be pleased with him) reported: The Messenger
of Allah (sallallaahu ’alayhi wa sallam) used to urge (the people) to
perform (optional Tarawih) prayer at night during the month of
Ramadan. He did not order them or make it obligatory on them. He
(sallallaahu ’alayhi wa sallam) said, "Whosoever performs (optional
Tarawih) prayers at night during the month of Ramadan, with Faith and
in the hope of receiving Allah's reward, will have his past sins
Regarding number of Rakah, I don't understand what you mean by short. Taraweeh is very flexible with respect to number of Rakah and it is not restricted to any number. In fact the Prophet (salallahu alayhi wassalam) would not increase it more than 11.
Narrated Abu Salama bin 'Abdur Rahman:
that he asked 'Aisha "How was the prayer of Allah's Apostle in
Ramadan?" She replied, "He did not pray more than eleven Rakat in
Ramadan or in any other month. He used to pray four Rakat ---- let
alone their beauty and length----and then he would pray four ----let
alone their beauty and length ----and then he would pray three Rakat
(Witr)." She added, "I asked, 'O Allah's Apostle! Do you sleep before
praying the Witr?' He replied, 'O 'Aisha! My eyes sleep but my heart
does not sleep." Bukhari Volume 3, Book 32, Number 230
The sunnah is to pray it in pairs of two and making tasleem at end of every two.
This is substantiated by what is related in the Two Sahih (authentic) Books of Hadith (i.e. Al-Bukhari and Muslim) from the Hadith of Ibn ‘Umar (may Allah be pleased with them) that the Messenger of Allah (peace be upon him) said:
(Optional) Night Salah is two Rak‘ahs followed by two Rak‘ahs (and so
on), and when one of you fears the break of dawn (Fajr Prayer), let
them offer a single Rak‘ah to make the Salah they have offered Witr
(Prayer with an odd number of units). [Sahih Al-Bukhari, Book on Friday, no.991]
Regarding, finishing Qur'an in 5-10 days, that is permissible. This is because, there is no prescribed period of time, except that it is best that it is not completed before three days. This is because of the hadeeth of Abdullah ibn 'Amr where Prophet salallahu alayhi wassalam told him
" He who finishes the recitation of Qur'an in less than three days
does not understand it." [Abu Dawud]
However, there is room of difference regarding that as well, since some scholars said this cannot be applied to Ramadaan. Imam al-Shafi'i was of the opinion that Qur'an can be finished every day or every night. What is necessary is that one should not haste but rather beautify the recitation of Qur'an and find peace in it.