Learn Wien's Displacement Law Derivation with Plainmath's Expert Help

The temperature of the surface of the sun
If I calculate the temperature of the Sun by replacing the effective frequency of the Sun (598 THz) in Planck's curve for Blackbody radiation, the result will be 10170 K. Still, in Wien's displacement law, the result will be 5778 K, is there an answer for this problem?

Is Planck temperature really the highest temperature?
Actually I was learning about Wien's displacement law. It states that
$\mathrm{\lambda <!--\; \lambda \; -->}T=2.898\times {10}^{-<!--\; -\; -->3}mK$
This is actually a part of Planck's law where the Planck's constant originated.
Now Planck's temperature is given as
$T_p=\sqrt{\frac{h{c}^5}{2\mathrm{\pi <!--\; \pi \; -->}G{k}_b^2}}=1.416\times {10}^{32}K$
Now Planck's length is $1.616\times {10}^{-<!--\; -\; -->35}m$
Now since the smallest possible wavelength is Planck's length, we can say wavelength of the electromagnetic radiation is Planck's length (Assume the energy doesn't create a black hole).
Now according to Wien's displacement law,
$l_{p}T=2.898\times {10}^{-<!--\; -\; -->3}mK$
Now solving this we get $1.79\times {10}^{32}K$, which is higher than the actual Planck's temperature.
Since this displacement law is completely derived from Planck's law, it bit frustrated me. I'm a bit confused. Is it the limit of the displacement law or my flaw?
Please rectify this.
(Sorry if I made any mistake. I'm new to this one. Please explain my mistake. I'm glad to hear that.)