Is it safe to use RAM sticks with different frequencies?

There are two things that can happen depending on the specific RAM modules
(brand, timing and motherboard compatibility),

1. The two modules will work effectively at the lower speed
   • this is safe and will only make you lose the speed edge of the faster module
     (besides losing the dual-channel DDR advantage, that is)
2. The modules will not be acceptable by your board together and it will declare memory failure.

The motherboard will make both RAM modules runs in the lower speed (unless you choose manual instead of auto RAM setting in BIOS), in this case 533MHz.

You system should be fine and you can use CPU-Z to check out the ram speed.

The short answer: you almost certainly won't hurt anything just by trying to install the two DIMMs together.

The potential problem is not related to using different frequencies of RAM; any motherboard will fall back to the speed of the slower memory module (DIMM).

The trouble you'll most often run into is most likely just an incompatibility between the two specific modules you're using, an incompatibility with your motherboard, or a flaw in your motherboard's design. Some motherboards also don't like it when you mix double-sided DIMMs with single-sided DIMMs.

If your computer doesn't boot with both DIMMs installed, you should try a few troubleshooting steps to figure out exactly what the problem is:

1. Double-check that both DIMMs are properly seated. Remove each one and reinstall it. Make sure it clips down properly.
2. Try running with each of the DIMMs separately (one at a time). If one of them doesn't work, that module is probably either defective or incompatible with your motherboard.
3. Try putting them in a different order on the board (i.e., swap which slot each one is in).
4. Try putting them in a non-interleaved (non-Dual DDR) configuration. If your motherboard has 4 slots and supports Dual DDR, you need to install pairs of similar memory modules in the appropriate slots. If your DIMMs are different sizes, or if one is double-sided and the other is single-sided, you should not install them in a Dual DDR configuration. Note, however, that some server-class boards always require you to install Dual DDR configurations.
5. If your motherboard boots with each DIMM individually but not together, boot with just one of them and go into the BIOS. Manually set the memory speed in MHz to that of the slower one. For DDR RAM, you might have to pick a clock speed that is half of the "rated" MHz, depending on the BIOS manufacturer. If you know about the other memory timings, you can also try fiddling with those.

Yes, it's a problem, but it totally depends on your motherboard and whether it supports it or not. If the system hangs, then put the RAM away as it might be harmful. The problem is that the faster module will revert back to the slowest module speed.