In episode 5, was the girl that spoke to the Hitachiin twins in hte beggining Haruhi?

That's right - I think the animators just made her look like Haruhi for sentimental reasons.

The दिखाना never कहा the flashback took place at a school. Besides they looked pretty young, they couldn't have been older than kindergarten age, I may be wrong but I don't think there is such thing as a private school for kindergarten and under. Even so, I'm pretty sure it was just a playground in the park.

And how would the death of Haruhi's mom affect anything? As long as it wasn't on the दिन of the funeral I don't think it would prevent her from being around other kids - in fact she could have been trying to make फ्रेंड्स to keep her from falling into depression. Actually the twins' refusal to play with her could have contributed to her serious nature - they didn't want to play with her so she insisted on doing the chores and shopping to keep her mind off of her mother's death (her dad already stated that she was too responsible/mature/independent for her age)

definitely right.. she's not haruhi..

It never कहा they were at school, and they didn't दिखाना the little girl's answer to the सवाल - she could have actually guessed correctly and if not then maybe she learned from it and that's why she was able to tell them apart so quickly. Also they implied that it was her at the end of the episode - Haruhi walked away from the twins and it shifted to the flashback of the little hitachiin twins on that park bench then showed the present twins standing in front of the same bench watching Haruhi walking away. I believe that it was Haruhi and they just didn't realize she was the same person until that moment.