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I have project and I would like to calculate the average of CPU activity (not usage, I need the average of CPU activity when it is not being used by a software) within a specific period of time. For example five seconds.

If CPU showed activity every second, then I can measure its activity within five seconds? how can I report that? where can I find it?

Another question: How can I find average CPU activity (not usage I need the average of CPU activity when it is not being used by a software) for one specific core for example core #1 within a specific period of time?

Average of CPU activity when it is not being used by any program is the idle time

With the command sar. for more information see sar man

The flag u in the command sar -u enables of reporting CPU usage of ALL CPU cores.
This gives the cumulative real-time CPU usage of all CPUs. Adding “1 5” to sar -u would reports for every 1 second a total of 5 times. Then sar will output the average. Something like this table:

$ sar -u 1 5
Linux 3.10.0-693.11.1.el7.x86_64 (pc.xxx.xxx) 10/12/2018 _x86_64_ (8 CPU)

01:40:51 PM CPU %user %nice %system %iowait %steal %idle
01:40:52 PM all 1.25 0.00 0.75 0.00 0.00 98.00
01:40:53 PM all 7.04 0.00 2.14 0.00 0.00 90.83
01:40:54 PM all 1.38 0.00 1.00 0.00 0.00 97.62
01:40:55 PM all 5.15 0.00 1.63 0.00 0.00 93.22
01:40:56 PM all 2.62 0.00 1.25 0.25 0.00 95.88
Average: all 3.48 0.00 1.35 0.05 0.00 95.11

In order to report the %idle average instantly, run this command:

sar -u 1 5 | grep "Average" | awk 'print $1" " $8'
Average: 96.27

The flag -P in sar -P enables reporting CPU usage of individual CPU core.

The command sar -P ALL 1 5 would measure average CPU Idle time for every core over five seconds.