Here's a possible solution. It involves storing the ending line number from the last six passes in a temp file. I'll leave the coding to you.

• First read in the line counts from the temp file into @linecounts.
• Get the starting point: $start = shift @linecounts
• On the pass through the log file iterate directly to the starting point: for (0..$start) {<FH>}.
• From there start parsing dates and log entries while incrementing $start with each line.
• Do whatever if entries found/not found
• Add new line count to array: push (@linecounts, $start)
• Rewrite temp file from @linecounts.
• Repeat in 5 minutes