What is the answer?

Can you be more specific?

Do the other numerics keep their sequence? (f.e. 12345 and 2345 1)
Or can you mix them up? (f.e. 12345 and 5342 1)

Is the 1 part of the original 5 digits (f.e. 12345)
Or dou you have a 5 digit number and you need the add the? (f.e. 23456 and 123456)

What 5-digit number has the following features?: If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.

There are lots of answers but how about

13267 x 3 = 39801

I think what you mean is, you have 5-digit number in the form of abcde, and the numeral 1 you put will make this a 6-digit number.

If you put 1 at the beginning, new number: 1abcde
If you put 1 at the end, new number: abcde1

If the latter is 3 times bigger, then we can form a simple equation:

3* 1abcde= abcde1
300000+30000a+3000b+300c+30d+3e=100000a+10000b+1000c+100d+10e+1
299999=70000a+7000b+700c+70d+7e
Dividing both sides by 7 -> 42857=10000a+1000b+100c+10d+e

So your 5-digit number is: 42857