If the ornithopter is played first turn, then ensoul artifact second turn can it attack that turn for 5?
Any thoughts....

Sure it can. Ornithopter has been under the battlefield under your control since the turn began, even though some of its stats may have changed.

Can someone clarify this for me?

Does summoning sickness end on my next turn or on my opponents turn?
example: I play creature on my turn, it has summoning sickness. My turn ends, my opponents turn begins, does my creature still have summoning sickness or no?

A creature is affected by summoning sickness unless it began YOUR most recent turn under your control.

So, essentially, summoning sickness ends on YOUR next turn.

302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.

yearofglad wrote:A creature is affected by summoning sickness unless it began YOUR most recent turn under your control.

So, essentially, summoning sickness ends on YOUR next turn.

302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.

Thank you for that clarification, I believe that this rule clearly explains the op question