Interference between 27MHz RX and 5.8GHz TX

You have to be careful with this kind of 'I'm on' signal.

A lot of regulations for un-licensed radio frequencies (such as the ISM band, etc) stipulate a maximum duty cycle on the transmission, meaning that you are only allowed to actively transmit for a certain % of the time. This prevents blocking of a particular frequency and allows better TDM of signals.

For example, for the ISM (Industrial, Scientific, Medical) range:

Dependent on the sub-band the transmission power is limited to 10 dBm … 27 dBm. The permitted time allocation (duty cycle) also varies with the sub-band. So interferences with other 868 MHz equipment are reduced and thus a better transmission quality can be achieved.

- ISM 433/868

So whatever solution you go for you will have to create some kind of periodic pulsed beacon that sends a short burst signal at pre-defined periods rather than just a constant 'on' signal.

This should also mean that you can save power in between the pulses as you can turn the transmitter off (a lot of TX chips have a 'sleep' or 'shutdown' mode) when it's not actively being used.

As has been mentioned in some of the comments, there is most likely a set of reinforcement bars in the concrete forming a 'Faraday cage'. This blocks a large number of signals from penetrating as they hit the bars and then get grounded by them. So, you need to pick a frequency that has a wavelength that is smaller than the space between the bars. Also, concrete can absorb the signal at certain frequencies.

From what I understand this is mostly due to the water content in the concrete. Water contains hydrogen. Hydrogen resonates at 2.4GHz. Many transmissions (WiFi for example) occur at 2.4GHz, so the hydrogen in the water in the concrete absorbs the transmission.^*

So, the ISM 868MHz band has a wavelength of about 0.35m - this is probably going to be way too big to fit between the bars (I'm not sure what the regulations state about bar spacing). ISM 915 takes it down to 0.33m - still too big. The 2.4GHz is 0.125m - much more realistic but may not get through the concrete. So you'd be looking somewhere in the mid-to-high 1GHz range. Personally I'm not aware of a license free frequency range in that area. You'd need to check with the RF licensing people in your area (FCC, OfCom, etc).

_{^*(This is purely my own conjecture - please correct me as I'd like to know the truth myself)}

Short answer: No.

Long answer: No, because the transmitter and receiver have to be tuned to the same frequency. You can't listen to Kool108 FM by tuning your radio to the frequency of 93X FM.

It is unlikely that a 9 dollar toy is designed to make it easilly retunable.