That isn't clear at all to me, I'm not sure what that means? I'm not blaming you, just the weird way it's worded.
So teams CAN talk w/ UFA players beginning today, but cannot sign them until July 5th? I thought it was weird how they kept advertising it during the draft as 7/5/13 being "Signing Day"...
There is conflicting information all over the place about the dates this year, but I don't think today is accurate. Pierre Lebrun and the actual CBA Doc say they can't talk to UFA's until July 3rd, and can sign on July 5th.
I think people are getting the dates confused with the normal dates for a non shortened season, that say they can talk to UFA's the day after the draft.
The July 3rd date is explicitly stated as part of the critical dates in 2012-13 though.
From CBA Page 358:
"EXHIBIT 16-B
2012/13 CRITICAL DATE CALENDAR
DAY DATE EVENT
Sunday June 30
x 2013 NHL Draft (Newark, New Jersey) (All 7 Rounds)48 hours after conclusion of the Stanley Cup Final
x First Buy-out Period Begins
x Deadline for First Club-Elected Salary Arbitration Notification (5:00 pm NY time)
Tuesday July 2
x Deadline for Qualifying Offers, which are not open for acceptance prior to July 5
Wednesday Thursday July 3 / July 4
Interview Periods for Club RFAs and UFAs (no SPCs or Offer Sheets with New Clubs)
Thursday July 4
x First Buy-out Period Ends (5:00 pm NY time)
x Club's ability to offer own potential UFA an eight (8) year SPC expires (11:59 pm NY time)
FridayJuly 5
x Qualifying Offers Open for Acceptance (12:00 pm NY time)
x RFA/UFA Signing Period Begins (12:00 pm NY time)"

From CBA Page 344:
"EXHIBIT 15 CRITICAL DATE CALENDAR
Day after the Entry Draft (but not later than June 25) until June 30
Unrestricted Free Agents may meet and interview with potential new Clubs, but may not sign new SPCs until the opening of RFA/UFA Signing Period
Later of June 25 or Monday after Entry Draft
Deadline for Qualifying Offers, which are not open for acceptance prior to July 1 (5:00 p.m. New York time)
Later of June 26
or Tuesday after Entry Draft
Restricted Free Agents may make contact with Clubs (including their own) regarding potential interest, but may not sign new SPCs or Offer Sheets until the opening of RFA/UFA Signing Period
June 30
Setting of Upper/Lower Limits
First Buy-Out Period Ends (5:00 p.m. New York time)
July 1
Qualifying Offers Open for Acceptance (12:00 p.m. New York time)
RFA/UFA Signing Period Begins (12:00 p.m. New York time)"