It might be difficult to attach a probability of error to entering numbers of a particular length, particularly because of psychological factors (temporarily remembering a 5-digit number, compared with an 11-digit number), but if we compare the number of permutations of 5 digits to that of 11 digits, we have a ball-park factor of 330,000 (11!/5!) to a million (10^11/10^5). A better way is to measure the number of mistakes made for both and do a proper statistical analysis.
But let's consider a comparison method. Let p=probability of mistyping a digit. The probability of successfully entering a 5-digit number is (1-p)^5 and of correctly entering an 11-digit number is (1-p)^11. The probability of making an error is P5=1-(1-p)^5 and P11=1-(1-p)^11 for 5- and 11-digit numbers. The comparison factor is P11/P5=(1-1+11p-55p^2+165p^3-330p^4+462p^5-462p^6+...)/(1-1+5p-10p^2+10p^3-5p^4+p^5)=
(11-55p)/(5-10p)=11(1-5p)/(5(1-2p) approximately if p is small=2.2(1-5p)/(1-2p).
Example: p=0.05, P11/P5=2.2*0.75/0.9=1.83. So P11=1.83P5, increased probability of error. If p=0.01 P11=2.13P5.
Let's take this further. 55 digits is equivalent to 11 5-digit numbers or 5 11-digit numbers. The probability of typing 11 5-digit numbers correctly is (1-P5)^11 so the probability of error is 1-(1-P5)^11; for 5 11-digit numbers it is 1-(1-P11)^5. If P5=0.2262 and P11=0.4312 (p=0.05), the chances of error are about 94% for each for 55 digits in total, but in one case 11 numbers have been typed but in the other case only 5 have been typed. This brings us back to a comparison close to 11/5.
The chances of error can be reduced by a factor of 10 by introducing a check digit. A check letter would be better because the error would be reduced by a factor of 26. This would, however, make an eleven-digit number into a 12-digit code, but the extra digit or letter would carry out some check on the digits entered. The check is programmed into the computer system so that if the number isn't entered correctly it would reject it, forcing the operator to check and retype it. A common mistake in typing is to transpose the position of two consecutive digits, but a check digit or letter can be used to reduce, but not eliminate, the chance of that happening, as well as reducing the chance of entering the wrong digits, regardless of their order. Checks that take into account order as well as the right digits are cyclic redundancy checks (CRC). Rather than just complaining to the supplier, why not make a suggestion to introduce such a check?
Let's take transposition as a common error. In a 5-digit number there are 4 pairs of adjacent digits, so if the probability that any one pair could be transposed is p, then the total probability of any being transposed is 4p. In an 11-digit number there are 10 adjacent pairs so the equivalent probability is 10p, 2.5 times higher. Other forms of error, like hitting the wrong key will also be proportionally higher.
If the numbers you are entering are, say, catalogue or part numbers, the system should know what each number refers to and feedback in words to the operator what item the number represents. But that could slow down data input and may be more of a distraction than an aid.
The supplier is faced with modifying software (at a cost, but the supplier will probably have had to pay for the system to change from 5- to 11-digit part numbers), but this may be cost effective because mistakes cost money! It's definitely worth discussing with your team leader or manager, or even with colleagues, as well as with the supplier.
