Good morning!
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おはようございます。
Good morning.
只今、五時半です。
It is 5:30 o'clock now.
今日は早起きです。
Today I am getting up early.
なぜなら今日は6時半に新宿まで家族を迎えに行かなければならないからです。
Because today I must go to meet my family at Shinjuku until 6:30 am.
なぜ迎えに行かなければならないかは、話がながくなってしまうので又の機会に話します。
I'll talk you why I must to go to meet them next time, because its story is so long.
そろそろ出かけないと間に合わなくなってしまいますので、出かけます。
Soon I will go out, because I don't have enough time.
では、またね。
So, see you.
Good morning.
只今、五時半です。
It is 5:30 o'clock now.
今日は早起きです。
Today I am getting up early.
なぜなら今日は6時半に新宿まで家族を迎えに行かなければならないからです。
Because today I must go to meet my family at Shinjuku until 6:30 am.
なぜ迎えに行かなければならないかは、話がながくなってしまうので又の機会に話します。
I'll talk you why I must to go to meet them next time, because its story is so long.
そろそろ出かけないと間に合わなくなってしまいますので、出かけます。
Soon I will go out, because I don't have enough time.
では、またね。
So, see you.

It is 5:30 o'clock now.
I might be wrong, but I think we only use "o'clock" for an hour without minutes. Like "five o'clock."
It is 5:30 o'clock AM now.
"o'clock" is only needed when it is an exact hour, eg. "5 o'clock", I added AM but it is optional to say it.
Because today I must go to meet my family at Shinjuku until at 6:30 am.
I think you mean to us "at" here instead of "until". "until" suggests that you will be meeting your family then leaving them at Shinjuku at 6:30 AM, but I assume you have arranged to meet your family at 6:30 AM.
I'll talk to you why I must to go to meet them next time, because its a long story.
Soon I will go out, because I don't have enough time.
This isn't incorrect, but I think I would use "Soon I will go out, because I'm running out of time." instead.
Because today I must go to meet my family at Shinjuku by 6:30 am.
I'll tell you why I must to go to meet them next time, because it's a long story.