Below are some common problems/answers.

This is probably due to a bad radio-connection (using same channel as WiFi?).

Most of the time this is either due to the fact that there's dirt (like hairs) stuck around the axis of the motor between the motor house and the propeller or that the propeller is too close to the motor so there's friction between the two. If neither helps check that the propeller is attached in the right way.

If there are other 2.4GHz devices (WiFi, Bluetooth, etc.) around there might be running on the same channel so try switching it in the bootloader configuration block. You can also try adjusting the radio bandwidth. If you set it to 250kbit/s you will get good range outside but inside the reception/range might become worse. Since the rate is lower the data spends longer time in the air which increases the probability of interference. Changing the speed to 1Mbit/s or 2Mbit/s will give better results under these circumstances.

There has been at least one case of broken Crazyradio antenna. To check if it is your case test briefly the connection without the Crazyradio antenna installed, if the range is the same then your antenna is certainly damaged (do not try the Crazyradio without antenna for too long!). Try with another antenna (any 2.4GHz Wifi antenna would do).

There's spare parts available at Seeedstudio

Try to flash the latest firmware using the instructions here and firmware here.

During the start-up all the mounted sensors run a self test. If either of these test fail it will cause the 5 red blinks. It is possible to see exactly what failed by connecting to the Crazyflie with the cf-client and open up the console tab.

The picture shows the console tab with no errors but when you have an error it might say e.g MPU6050: Self test acc Y [FAIL]. low: 0.300000, high: 0.949999, measured: 0.0. This example means that the accelerometer Y axis didn't pass the self test and is probably defective. It is possible to get this error also if the Crazyflie is moved to much during the self test so try putting it on a sable surface before you power it on.

Another thing to try, if you get an accelerometer self test error with measured value 0.0, is to tap/bang it on the sides. E.g. use a table edge to tap/bangit against, and tap/bang the rounded corners of the PCB (where the LEDs are). This could in theory release the accelerometer lock-up. If you managed to fix it this way please let us know as well because it is just theory now.

If anything of the above didn't fix it you probably have a broken sensor and the sensor needs to be replaced. Contact Seeedstudio customer support and they will help you out. You can also visit the forum and especially this thread.