I would be with
@PGF2016 on this. 5k emergency fund is a bit low. General consensus is around 6 months living expenses is a good target. In your case this is 15k plus whatever pension contributions you wish to make, so around the 25k. You have the option of paying 10k off the mortgage in a lump sum, but that really is up to you.
The quick maths are you pay just shy of 1500 a month on the mortgage. The total cost of the mortgage is 625k. The balance after 5 years is 331k and 10 years is 297k. You are mortgage free in 35 years, so when you are 65.
If you were to overpay by 1000 a month, you become mortgage free 19 years earlier [so when you are ~44]. The total cost of the mortgage reduces to 468k. The balance after 5 years is 266k and after 10 years is 154k.
I would definitely not consider building any more savings in the short term. You have enough given the interest rate you are paying on your mortgage, and your return on your savings.
Personally, if I was to start a pension, I would keep the contributions relatively low enough to start with - maybe 500 euro a month net/850 euro gross. This gives you 1500 to put against your mortgage say for 5 years, and then change the distribution to put more against the pension, ending up with a more 50/50 split as you hit 40. Once the mortgage is clear you can then put more into the pension should you wish.
Paying 1500 extra off the mortgage for 5 years would bring the balance down to around 233k after 5 years.
All this is of course based on the assumption you don't have a master plan to retire at 45 etc.
The other thing I would say is you don't have any dependants currently. This can of course change over time, and you would need to review it in this case.