Can this be really solved?

Algebra Level 5

x57x41=0\large {{ x }^{ 5 }-7{ x }^{ 4 }-1=0}

If r1,r2,r3,r4,r5r_{1}, r_{2}, r_{3}, r_{4}, r_{5} are the roots of the equation above, find the value of expression below.

1r120+1r220+1r320+1r420+1r520\large{\frac { 1 }{ { r }_{ 1 }^{ 20 } } +\frac { 1 }{ { r }_{ 2 }^{ 20 } } +\frac { 1 }{ { r }_{ 3 }^{ 20 } } +\frac { 1 }{ { r }_{ 4 }^{ 20 } } +\frac { 1 }{ { r }_{ 5 }^{ 20 } } }

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