I have YOYO-1 dye and I want to add dye at 5:1 ratio. And I am using a plasmid of length 5411 bp. Please tell me how to calculate this ratio to get a volume of dye to be added to DNA of 1 microgram.
If you mean molar ratio, you have to calculate the molar amount of 1 ug of 5411 bp DNA. It can be easily approximated with 660 g/mol per base pair, i.e. 1 ug of 5411 bp corresponds to 0.000001/(5411x660)=0.28 pmol. However, in your experiment you need to keep constant ratio of the dye per base pair, so the length is not important here and you just calculate 0.000001/660=1.5 nmol (of base pairs). So you need to add 7.5 nmol of the dye.
You don't care about plasmid size. Just measure the absorbance @260 nm, which is directly related to the concentration of DNA (and thus base pairs), and add dye accordingly.