[1:5] God-human relationship

"iyya-ka na3budu = You-alone, we worship
wa iyya-ka nasta3een" = and [from] You-alone, we seek help [1:5]

This explains our relationship with God. We are dependent on Him alone (and nothing else).  We are independent of all others (apart from Him).

So if we seek help from others, we should do it while knowing that any help we receive is by the permission of God. If He doesn't permit it, all the help in the world would not make a difference.  .

But-notice the phrase order of this verse:
"You-alone, we worship and You-alone, we seek help"

1. worship Him alone
2. seek Help from Him alone

It doesn't say seek Help first, then worship second.  Specifically it mentions worship first, seek Help second.  So our worship should not be seen as a payment in order to invoke God's help.  this is insincere. 

We should worship Him because He is our Lord and Lord of the Worlds, our King and King of Judgment Day, He is The Merciful Merciful, He is  God and we are His servants, His creation.

Remember:
God does not need our worshipping nor our prayers!

O mankind, you are those in need of God, while God is the Free of need ... [Quran 35:15]

Then why must we pray?  Like all of God's commandments for humanity - God doesn't make us do something that is bad for us, or that does nothing for us.  He is Merciful.  He commands us to do things that are good for ourselves or for others and humans as a whole.  

Just looking at one aspect of prayer - the psychology - the act of holding our chin up and head up high is to show pride!  Therefore, the act of putting our face to the ground (during prostration), a place lower than our bums, is the most humbling position we can be in.

 so psychologically (mentally) it teaches us:

• humility
• order (standing in rows)
• unity (close to brothers, all facing the same direction)
• punctuality (5 daily prayers at specific times)
• etc...

as well as the physical (many positions in Yoga are similar) and spiritual benefits.