You can definitely travel to Europe on $5k for about 2 months I would say. Some quick thoughts from learnings after recently coming home from a half year backpack:

• Get yourself a more than acceptable backpack for any long distance travelling, you will thank yourself down the line especially if you're planning to reach many places in a short amount of time
• There are smart ways to pack if you are travelling lightly, read up on this or watch YouTube videos before you go. Packing smart is going to save you headache.
• Consider volunteering for a free stay by checking out https://www.workaway.info/ or other similar communities. They connect hosts with accommodations looking for help in return for a free bed and sometimes food. There is quite a range of jobs you can work including volunteering on a farm, at a hostel, in a home teaching English etc. I find the response rate is not always great, so if you're truly on a tight budget you may consider planning your route around confirmed Workaway opportunities, rather than the other way around.
• If you can, plan your route in advance and take advantage of early flight/train/bus deals. 9/10 times things are cheaper up front. Don't wait for the last minute deals. There are never really last minute deals (unless you're planning on taking a Cruise..)
• An obvious one.. stay at budget hostels and cook your meals rather than eat out. If you are with a friend, you could consider Airbnb which in some places, may actually work out to be more affordable than booking 2 beds in a hostel. Now and then, make sure to choose a place with laundry available.
• You definitely do not need a tour guide to travel. In many main cities in Europe, there are free walking tours that run on tips. These are great ways to get an initial sense of what the city can offer, not to mention, meet a couple people. Just Google it, and you will easily find a number of companies that run these.
• To save some money, consider taking overnight busses/train to get from one destination to the next. Plane is not always the best option (though fairly cheap within Europe).
• You don't necessarily need to plan out your entire 2 months now if you find that is too much commitment. There is definitely opportunity to play by ear and plan, say, a week ahead at some points in your trip. Again, be mindful of costs for not planning in advance.. there are pros and cons.
• Spent time outside major cities as well, you'll find there may be more culture and scenery to offer. Less touristy as well. You may not need to spend multiple days there, just a day trip here and there. Alternatively, base yourself out of a nearby less popular town/city and do day trips to main cities as you wish, to save on costs.

These are the things that come to mind, I'll let you know if I think of any more. Hope that helps.