Harmonics below oscillation frequency in the brain
You explain in the comments that the signal is sampled at 50 KHz, then low pass filtered at 128 Hz with a 2nd order biquad filter and then resampled and stored at 256 Hz. 

If you weren't prudent with choice of sampling rate and low pass filtering, then the harmonics of 10 Hz could create a component at 5 Hz through aliasing. For example this would occur if you used a sampling rate of 25 Hz: the third harmonic at 30 Hz would fold to the 5 Hz frequency. I explain aliasing in more detail at this post here:

Where should I set my anti-aliasing filter corner frequency for this signal?

That said, there are two prominent mechanisms that could create folding images in vicinity of 5 Hz due to aliasing during this sampling process.

The first would be due to interference components above the Nyquist frequency of 25 KHz prior to the sampling of the analog signal - specifically any frequency components at $N f_s \pm 5$ Hz would fold to 5 Hz in your digital signal where $N$ is any integer and $f_s$ here is 50 KHz. (So 50 KHz +/- 5 Hz, 100 KHz +/-5 Hz are example locations where interference can alias in). To avoid this be sure to use a good anti-aliasing filter and pay particular attention to its rejection around $N f_s \pm 5$ Hz with a rejection band around those frequencies that are within the frequency range that you want to maintain to be free of interference for your measurement.  Given this is many of orders larger than your 10 Hz interference, it is less likely this is an issue however should not be discounted depending on your measurement sensitivity desired.    

The second mechanism, and likely dominant one in this case, is your resampling approach. Resampling to 256 Hz is a fractional rate conversion from 50 KHz and there could be many opportunities to create harmonic folding effects. The actual implementation needs to be reviewed in detail including significantly the performance of the resampling filter prior to decimation. Resampling to 256 Hz is identical to sampling at 256 Hz directly, so any frequency content above the Nyquist frequency of 128 Hz would fold into band. Specifically in this case the frequencies at $N 256 \pm 5$ Hz would land at 5 Hz in the digital domain.

Without seeing the actual implementation or ability to change it this would be difficult to predict although certainly can be measured. Induce a 10 Hz test signal with high harmonic content (impulses) and measure the results without your actual device you are measuring connected to assess your measurement noise floor in that condition.   

Regardless of aliasing, to be sure that the interference itself does not contain 5 Hz components, I would also recommend analyzing a measurement without your true data source connected (such that you are only evaluating background noise). This would also give you a fidelity of your measurement system in showing you what sensitivity can be achieved, and the related confidence of your results.