What is the minimum transaction fee I can put manually ? I want to send 0.00005btc. I don't care if it takes more hours to be done.
Bitcoin-core v.0.11.2 now requires at least 0.00005BTC as TX fees.
No, paying a lower fee is perfectly fine your TX just counts as "free" (as in: one without fee).
If you don't include this minimum fee, your TX risk the chance of not being relayed to other nodes on the Bitcoin network. Most miners have upgraded to v.0.11.2 also, therefore may not include your TX in their block - leaving your TX out there not being confirmed or even being relayed to other nodes.
Bitcoin helps you being "free" of banks - it was never intended to be a "free" network to send money. Put the minimum fee required.
PS: If you want to send just a 0.00005 BTC transaction, you are spamming the network.
If it was never intended to allow free transactions, why is there a priority system in the first place?
Yes, it is not recommended to pay a low or no fee at all, but its possible and the transaction will get relayed by nodes. Maybe not on the first attempt, but if you keep rebroadcasting it, it will reach miners. Miners - again - may take some time to put it in a block (think days, not hours), but eventually will do it. If you are perfectly fine to wait a few weeks for your transaction to confirm, its perfeclty viable to create it without fee. Keep in mind that you will need to rebroadcast the transaction from time to time, once or twice a day should be enough.
A single TX without fee is hardly spam.