The Molad for Sivan is Monday, May 18, 2015, at 2:11 pm and 5 chalakim.
Rosh Hodesh Sivan is Monday evening, May 18th, and Tuesday May 19th.
What are Chalakim?
Chalakim (חלקים) is plural of the Hebrew word chelek (חלק). A chelek is a part. In this context, a chelek is the smallest unit of time in the Jewish Calendar, and is equal to 3 1/3 seconds. There are 18 chalakim in a minute, and 1080 chalakim in an hour, and 25,920 chalakim in a day.
The Jewish Calendar is based on lunar months. A lunar month is one revolution of the moon around the earth, and for the Jewish Calendar, one lunar month is 29 days, 12 hours, 44 minutes and one chelek. In the Jewish Calendar, a month can be either 29 or 30 days.
The date of Shavuot is the 6th of Sivan (and the 7th of Sivan outside of Israel). This is the only holiday that does not have its date specified in the Torah. The date of Shavuot is specified as 50 days after Pesach.