One way to do this is to use the lowest common denominator of the factions. First, though, 6/8 can be reduced to 3/4. Since the LCD of 4, 5 and 10 is 20 and there are no other common factors in the other denominators, the LCD=1820 (=20*13*7). We then multiply each fraction by 1820, and write down the answers: 1260, 1365, 1092, 1274, 1300. These are easy to put in order: 1092, 1260, 1274, 1300, 1365. We now arrange the associated fractions in the same order: 3/5, 9/13, 7/10, 5/7, 6/8 (3/4). [When we multiply each fraction by 1820, we divide the denominator into 1820 and multiply the result by the numerator.]
Another way is to convert each fraction into decimal and compare decimals. We only need a couple of places of decimals to make the comparisons: 0.69, 0.75, 0.60, 0.70, 0.71. This is the same as comparing: 69, 75, 60, 70, 71. The order is 60, 69, 70, 71, 75.
An easy way to organise the fractions is to write the fractions on separate pieces of paper. On the back of each piece of paper write the number you are going to use in place of the fraction. Now you can easily arrange the papers in order according to the order of the replacement numbers. All you have to do then is to turn the papers over to see what the fraction order is.