Is Jihad a pillar of Islam?

What are the pillars of Islam? Some say “Jihad” is a pillar of Islam and Kalima Shahadah is not. Is that true?

There are five pillars of Islam. And these are:

1-Kalima Shahadah, Testifying (the fact) that there is no god but Allah, that Muhammad is His bondsman and messenger

2-The establishment of prayer

3-Payment of Zakat

4-Pilgrimage to the House (Ka'ba)

5-The fast of Ramadan.  

“ Narrated Ibn 'Umar: Allah's Apostle said: Islam is based on (the following) five (principles): 1. To testify that none has the right to be worshipped but Allah and Muhammad is Allah's Apostle. 2. To offer the (compulsory congregational) prayers dutifully and perfectly. 3. To pay Zakat (i.e. obligatory charity) . 4. To perform Hajj. (i.e. Pilgrimage to Mecca) 5. To observe fast during the month of Ramadan.” (Bukhari, Belief)

“It is reported on the authority of Ta'us that a man said to 'Abdullah son of 'Umar (may Allah be pleased with him). Why don't you carry out a military expedition? Upon which he replied: I heard the messenger of Allah (may peace be upon him) say: Verily, al-Islam is founded on five (pillars): testifying the fact that there is no god but Allah, establishment of prayer, payment of Zakat, fast of Ramadan and Pilgrimage to the House.” (Muslim, The Book of Faith)