FAS sight calls the whole shootin' match of Iranian (and North Korean) missiles liquid fueled. There is no evidence that the Shahab-5 has ever even been flight tested. I strongly doubt that the Iranians are close to making a solid fueled missile. Solid fueled IRBM are a vastly more difficult to make (and tactically more effective) than liquid fueled.
I know that the Iranians claimed to have made a solid fuel IRBM of some sort, they say a lot of things I'm not buying.
That point is at least arguable. I worked on Titan I and the commplexity of piping to cool the nozzles, the turbine pumps for fuel and LiquidO2, the requirement to vent the O2 boiling off before launch, the thermal expansion and contraction issues from 273 deg Kel to 6,000 deg F, all make it a very difficult bird to manufacture and launch.
A solid fuel missile is basically a pipe with a mixture of an oxidizer and fuel that has been solidified. Put a few thermite firecrackers in the azz end and you got yourself a rocket. A bit of an oversimplification....maybe, but you get my point.