if the deposits will be done often, if you go over 5k€, you will have to provide information on source of the money and purpose of the money. also if they are part of business transaction(B2B, B2C) you CANNOT use more than 5k€ cash. it is simply forbidden. i am not sure if it is EU-wise or only in selected countries.
if it will be only the initial capital for the company, one-off payment, i think you should be able to put in more than 5k€ but you still will have to provide source of the money because that is tied to he amount itself. you don't need any proof, you just tell them when they ask but they might not accept the reason(note that if you withdraw large sum, they will ask for source and purpose of the money and can prevent you from taking them out and possibly alert authorities to investigate. i wanted to withdraw 15k two times from two different branches and one was ok with just "for personal use" and i had to argue with the cunt in the other branch before she approved it).
so based on the purpose and your conditions, that you have not provided here, just pick a bank and ask them about these things. i think there will be some variations in different countries but in general this is how things are today. all of this is defined in the laws so you can simply look it up yourself for individual countries because they have to follow the EU legislation.
in essence, the entire system is setup so people don't use cash so everything can be traced through bank transfers under the bs of "money laundering". right now the hustle-free limit i 5k but i heard that might change so ... f**k EU