In 5 weeks you can see quite a lot of Scotland without having to rush from one place to the next. As the previous commenter says, the rail network and bus services are pretty good, not to mention the ferries. In addition to the RS guide, take a look at http://www.undiscoveredscotland.co.uk/index.html for ideas.
Here is a suggested list of destinations, just FWIW. I'll assume you are flying in & out of Edinburgh.
Spend your first 3-4 nights in Edinburgh. Take a day trip to Roslin Chapel (about half a day, by bus -- buy a day pass and you can use the bus again in the evening to go our for dinner).
Next, Stirling and onward to Glasgow. How many nights you spend in Glasgow depends on your interests. Heading north from Glasgow, stop at Luss (bus) or Tarbet/Arrochar (train or bus) to enjoy Loch Lomond. The boat trips on the loch may still be running; check Cruise Loch Lomond and Sweeney's.
Continue by bus to Inveraray, at least 2 nights (I can recommend Brambles for lodging and the George Hotel for dinner). Inverary Castle is beautiful and the town has good shopping for Scottish woolens. By bus you could take a day trip to Lochgilphead & Kilmartin Glen or onward to Tarbert, which has a ruined castle associated with Robert the Bruce. On the same bus route is the Auchindrain Township outdoor museum -- a must if you're interested in the history of ordinary people.
Next, Oban and ferry connections to the Hebrides, maybe 4-5 nights? And then Fort William and the Jacobite Steam Train. Depending whether you want to deal with the fairly inconvenient public transportation on Isle of Skye, take the Mallaig ferry to Skye or else return to Fort William. There's plenty to see around Fort William with Glencoe, Fort Augustus, etc. so plan 3-4 nights.
Now you go along the north shore of Loch Ness, stopping at Urquhart Castle and the Loch Ness Centre & Exhibition. Stay in Inverness 3-4 nights and take a bus to see Culloden Battlefield and Cawdor Castle.
By train from Inverness you can travel south on the main route to Pitlochry. Along the way are Dalwhinnie (distillery tour) and Blair Atholl (Blair Castle).
Head east to Dundee and onward to St. Andrews if you have any interest at all in golf. The British Golf Museum is great, even for a non-golfer, and the Old Course Hotel is not all that expensive (and it has an indoor swimming pool).
Return to Edinburgh and Bob's your uncle! (I haven't added up the nights, but I'm sure this is all doable in 5 weeks.)