Convert Planck unit to SI metric

Python 3, ^{118 \$\cdots\$ 85} 80 bytes

Saved a whopping 29 bytes thanks to Surculose Sputum!!!
Saved 4 bytes thanks to Arnauld!!!
Saved 5 bytes thanks to xnor!!!

lambda a,b,c,d,e:399674e26**e/174539e29**a/162874e3**b/523253e37**c/189007e13**d

Try it online!

Jelly,  35  34 bytes

“~VHð¡ȷ‘I⁵*ד®ƬØʋ¥4ẋİ8nCaḌ’bȷ6¤*⁸P

A monadic Link accepting a list of the five exponents, [L, M, T, Q, Θ], which yields a floating-point number.

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How?

“~VHð¡ȷ‘I⁵*ד®ƬØʋ¥4ẋİ8nCaḌ’bȷ6¤*⁸P - Link: list of numbers       [L, M, T, Q, Θ]
“~VHð¡ȷ‘                           - list of code-page indices   [126, 86, 72, 24, 0, 26]
        I                          - differences                 [-40,-14,-48,-24,26]
         ⁵                         - ten                         10
          *                        - exponentiate                [1e-40, 1e-14, 1e-48, 1e-24, 1e26]
                              ¤    - nilad followed by link(s) as a nilad:
            “®ƬØʋ¥4ẋİ8nCaḌ’        -   base 250 number           572938613971191112529082399674
                            ȷ6     -   10^6                      1000000
                           b       -   convert from base         [572938,613971,191112,529082,399674]
           ×                       - multiply (vectorises)       [5.72938e-35,6.13971e-09,1.91112e-43,5.29082e-19,3.99674e31]
                                ⁸  - chain's left argument       [L, M, T, Q, Θ]
                               *   - exponentiate                [5.72938e-35^L,6.13971e-09^M,1.91112e-43^T,5.29082e-19^Q,3.99674e31^Θ]
                                 P - product                     5.72938e-35^L×6.13971e-09^M×1.91112e-43^T×5.29082e-19^Q×3.99674e31^Θ

Fortran (2008), 133 bytes

At least for this challenge there should be a Fortran solution.

Takes input as integer array.

real(real64)function h(I)
use iso_fortran_env
integer I(5)
h=product([572938d-40,613971d-14,191112d-48,529082d-24,399674d26]**I)
end

A slightly longer and less accurate function uses the logarithm (stolen from @xnor):

real(real64)function f(I)
use iso_fortran_env
integer I(5)
f=exp(sum([-7884487d-5,-1890850d-5,-9836347d-5,-42083140d-5,7276562d-5]*I))
end