If x+1/x=5 then findout the value of x^5+1/x^5=?

• given,(x+ 1/x) = 5
  
  x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1)
  
  x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)
  
  multiplying (1)& (2), we get
  
  =>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
  => x^5 + 1/x + x + 1/x^5 = 2530
  => x^5 + 1/x^5 + (x+ 1/x)= 2530
  => x^5 + 1/x^5 + 5 = 2530
  => (x^5+ 1/x^5)= 2525
  
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