5 weeks - Berlin-Dresden-Prague-Budapest-Ljubljana-Florence-Rome

You have a sensible number of cities for your timescale. Rome and Berlin IMO merit a little longer than your average length of stay and Ljubljana, being compact can be seen in a couple of days. Four days for each city maybe slightly less, accounting for travel time is OK. For a trip of this length, you may want a down day somewhere in the middle just to recharge your batteries.

Use seat61.com for train travel ideas. There aren't many flights from Prague to Budapest, so book asp for the best prices. However, Budapest to Ljubljana is a tricky journey - no direct flights or nine hours on a bus. It is no better if you try to fly to Budapest first then hit Prague. Use rome2rio.com to check routes, but from what I can see, getting to Ljubljana is going to be a problem. From there, it's 6 hours to Florence by train or 8.5 hours by bus (again, no direct flights). How keen are you to get to Ljubljana?

If you are taking any flights within Europe, book these asap as prices only head one way. Book rail tickets in advance too.

There is a daily train from Budapest Deli station to Ljubljana taking 8 hours.
It will be easiest to meet your friend in Florence as you will be traveling in from different directions.

Thanks for the helpful advice, Jennifer!

One of the earlier plans I had was to skip Budapest as it was a abit out of the way from the direction that I was traveling; that is Prague - Vienna - Salzburg - Ljubljana (this would be about the middle of the trip for some down time) and down to Milan. However I wasn't sure about passing up Budapest, hence the switch.

Alternatively is Prague - Vienna - Budapest - (fly in) Milan. That seems to be the most logical route..

No Venice?

Lucky you, with 35 days. I'd try something along these lines.

Berlin - 5 nights
Dresden - 3 nights
Prague - 4 nights
Vienna - 3 nights
Budapest - 5 nights
Via Zagreb to Ljubljana - 3 nights
Via Trieste to Venice - 3 nights
Florence - 4 nights
Rome - 5 nights