I am starting up the Lost Mine of Phandelver campaign with five players. We are starting out now but I am already thinking about how to bridge these characters with Hoard of the Dragon Queen (since I already purchased the book). Thoughts? How should I change the second half of LMoP to set us up for HotDQ? How should I modify the first half of HotDQ? Is there a guide somewhere? I don't mind working through it on my own but I thought I'd look elsewhere first. I'll post a link to the modifications summary if I do it on my own. 
I have not played LMoP, so I can't answer the fluff aspect... how to get them to travel from one place to the other. HotDQ does have some back ground and Hooks that your players could use to make the tie in.
As for mechanics... I would try and not let them reach lvl 5 in LMoP, keep them around 5500XP (Personally, I would even fudge the XP gains if I had to.) Being 4th level means Ep1 and Ep2 will be somewhat easier, but still not a cakewalk. Ep1 you could just up the monsters a bit, use some better tactics, and have them go on more of the missions... it will still be a challenge for them.
Hitting Lvl5 right before or during Ep3 isn't that big of a deal. Again, you can buff some of the encounters if you want. But there are still things they will need to think instead of fight...
But I would not skip any of he Episodes... they give the adventure more depth.
(If you fudge their XP, and feel bad about it, you can always give them more later. Plus, the guidelines for XP in Ep4 is stupid high for some menial stuff...)
I did this exact thing - I first ran Mines of Phandelver and then transitioned into Hoard of the Dragon Queen. It's doable but not exactly the easiest thing.
During Mines of Phandelver, I'd try to limit overall XP gained so that players are about level 3-4 entering the final "dungeon crawl." To do this, I'd eliminate some of the side quests in Phandelver and greatly reduce random encounters that don't really challenge the party but give them an XP bump.
This isn't essential, but what I then did was have the characters take an entire year off in-game between the two adventures. This allowed the characters to do the things listed in the "downtime activities" such as training for multiclassing, selling magic items, working jobs, and pursue their individual backstory. To do this, I actually ran solo session with each of the players. During this downtime I laid hooks for the upcoming adventure. Since the beginning of Hoard of the Dragon Queen is 750 miles away from Phandelver, I enticed each character to travel to the town at the beginning of HotDQ. I ended each solo adventure with each character traveling to the town that Dragon Queen starts in. We reconnected at the gaming table and reunited the party just before the action starts in Dragon Queen. This worked out beautifully for the party and it was really need having the characters "reunited" with a bunch of secrets and new developments to share (or not) with the rest of the party.
Hoard of the Dragon Queen's beginning is quite harsh so it was about right for 4th level characters, actually. Once again, however, I cut out some of the events in the initial chapter to reduce the rate of experience gain. It was really fun for the characters to mow through a bunch of kobolds, however. I also eliminated random encounters in the third chapter and reduced the number of opponents in general to slow down XP gain. One other thing I did to reduce the rate of expereince gain was to give the party an NPC member which siphoned off 1/5 of the XP.
The goal is to get the characters back on track level-wise by the end of the Hoard of the Dragon Queen. By about chapter 5-6 you should be able to accomplish this.
I hope this was helpful! Good luck!
Thanks for this thread. I was planning something similar for my group too and its good to have some ideas, so I bring them into it with my eyes open.
I am still toying with a few side adventures to get them up to around level 6, starting HotDQ with new level 1 characters and then somehow work in their existing characters when both groups are similar levels.
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