Each can be done in a couple different ways; but, for example, if you do #2 by multiplying first, you need to be sure to multiply every term; subtraction first is more direct.
I'll demonstrate a couple ways #2 could be done:
Following the order of operations in reverse, starting with [imath]\frac{x}{5}+3=5[/imath], we would first undo the last operation on the left (addition) by subtracting 3 from both sides; we get [imath]\frac{x}{5}=2[/imath]. Next we would undo the remaining operation (division) by multiply both sides by 5: [imath]5\cdot\frac{x}{5}=5\cdot2[/imath], so that [imath]x=10[/imath].
Often we prefer (as pka showed) to clear fractions first, largely because working with fractions is more error-prone. This time, starting with [imath]\frac{x}{5}+3=5[/imath], we would first multiply both sides by 5. But that means we multiply the
entire left side and the
entire right side by 5, which many beginners forget to do. That is, we are doing this: [imath]5\left[\frac{x}{5}+3\right]=5[5][/imath]. Distributing on the left, this becomes [imath]5\cdot\frac{x}{5}+5\cdot3=5\cdot5[/imath]; we've multiplied
every term. Carrying this out leaves [imath]x+15=25[/imath]. Now we undo the remaining operation (addition) by subtracting 15 from both sides, leaving [imath]x=10[/imath].
We get the same result both ways, as long as we do the work correctly. In some cases, as in #5, clearing fractions is the same as following the reverse order of operations, because the last operation performed in evaluating is the division, so you undo that first anyway.