Both explorers show two different time stamps. "Received time" is the time that the transaction was first seen by the block explorer (relayed over the peer-to-peer network). "Mined time" (shown by blockchain.info under "Included in Blocks") is the timestamp of the block in which the transaction was included. You'll note that both explorers agree about the mined time as being 12:05:22 UTC (note blockexplorer.com is displaying it in your local time zone, which I guess is UTC+1).
For received time, blockchain.info shows 12:00:17 while blockexplorer.com shows 12:05:22 (same as mined time). So one possibility is that the transaction was actually created and posted to the peer-to-peer network at 12:00:17 (or earlier), and blockchain.info received it over the network at that time. But for whatever reason, the transaction didn't make it to blockexplorer.com over the network; it didn't see the transaction until it got the block in which the transaction was included.
It's hard to guess why that would happen. But it appears from the screenshot that this might be a non-standard transaction, which most nodes will not relay. Maybe blockchain.info is better connected to those few nodes which will relay them.
1Can you post screenshots and IDs? Are you talking about blocks or transactions? Are you talking about the actual timestamp in the block, or the time that the explorer received it (some list both)? Finally note that blockchain.info appears to show times in UTC while blockexplorer.com tries to use your local time zone. – Nate Eldredge – 2016-10-26T12:25:42.443
Check https://postimg.org/image/y06qca7sd/and https://postimg.org/image/ukpwqy1pd/ Ok, since blockexplorer uses local time and blockchain.info UTC, there's still a gap of 5'.
– mvanderbilt – 2016-10-26T12:30:09.903Can you also give the transaction ID here? Can't copy and paste from a screenshot. – Nate Eldredge – 2016-10-26T12:44:05.893
tx 8165e70d1904c4b8e10eaf1029ab2ced0134e09f2e4212df3ae4ba2097c02874 – mvanderbilt – 2016-10-26T13:19:52.097