You would need a 13 amp fuse in that mate a 5 amp will just keep blowing under the load you will put on it.
Having said that if it was working with a 5 amp then it should continue to work with it.
Checking for faults before upping the rating might be advisable.
It may just be over zealous demo rules that downrated it for those purposes.
Also how long is the run to your shed from the distribution box etc lots of factors to take into account that were not necessarily the conditions it was previously used in.
If you are not happy with the help you received from the supplier, tell them, and tell them they will be getting it back if you continue to be unhappy.
The purchaser has a contract with them and that contract gives them the right to expect goods to work and to do so without you tampering with it.
The seller has a duty to ensure that contract is fulfilled ex display or not.
If you do go this route then do not change fuses or otherwise interfere with the machine outside normal operating instructions, it may void your rights as a consumer.