Thank you for the opportunity to help you with your question!

Perimeter of the triangle p = 66

The sides of the triangle are : 5x, 3x-1, 4x-12

Perimeter means distance all round i.e. summing all sides

(5x + 3x-1 + 4x-12)=66

5x+3x+4x-13=66

12x-13=66

12x=66+13

12x=79

x=79/12

x=6.6

side1:5x=5*6.6=33

side2:3x-1=3*6.6-1=18.8

side3:4x-12=4*6.6-12=14.4

Shortest has length is 14.4

Its not clear to me what you meant by x5, i have taken it to be 5x, if this not correct, please send me a follow up correction with correct information, then i will solve it again

Please let me know if you need any clarification. I'm always happy to answer your questions.