I own both Traveller 5 and Mongoose Traveller Core Rule Book (the newest one that is only available in PDF). I'm struggling with grasping all of T5, so I'm looking at using MGT. One of the things I feel I need to run the campaign that I want is a propper ship building system. I know that Mongoose is releasing a system for that later this year, but while waiting I was wondering if T5 ship building system is compatible with MGT, and if anything what I need to change to be able to use it.
No, they're not compatible. T5 followed a rather different design philosophy to MGT2, and the games have rather different mechanics. While the two games share a lot of setting conceits, they're different enough rules-wise that detailed mechanical conversion of a ship from one game to the other is too hard to be worth it.
T5 ship creation features a number of subsystems and mechanics that are... Um, complicated, and not accounted for in MT2. (For example, a T5 ship could have a jump drive that's highly experimental, and therefore takes up more space and costs more and has different requirements than a standard drive with the same jump rating; T5 treats life support systems and living space as requiring separate facilities; And of course, T5 supports generating full QREBS for all components.) You could conceivably strip out all the extra T5 detail and options in order to build a T5 ship that works in MGT2, but for that you'd have to be intimately familiar with what is and isn't possible in both systems, and you won't be until MGT2's shipbuilding rules are released.
On the other side, MGT2 has one major ship mechanic that there are no rules for in T5: Power. To convert a T5 ship to a MGT2 ship, you'd need some way of calculating how much power it has available and consumes, and to the best of my knowledge there's not yet any available resource that would allow you to do this.
In short, you're out of luck. You'll just have to use the pre-designed ships included with MGT2 for now.
GMJoe's answer is accurate. However: to a certain extent, they are compatible. First, both systems derive from classic Traveller, and so ship designs are relatively portable. However, the relationship goes a bit deeper, in that drive rules in MGT2 are derived directly from Traveller5.
Let's put it this way. Unless your game is going to hinge on highly technical details around starships, T5 ships will work fine with MGT2, and vice versa.
Extended Boring Discussion
Drive Percentages Same
(With the exception of power, which see)
When MgT2 was created, I pushed hard for them to use T5's M-drive and J-drive percentages, and they were adopted. That alone guaranteed that ships were more inter-compatible than other systems, allowing components from either system to be added-on and the resulting ship to be "broadly" compatible, if not perfect. For most Traveller games, the differences fall below the resolution of the game.
Additionally, I was less worried about "accessories" such as weapons, sensors, emplacements, etc, as they are customizable in T5. T5 has a lot of ways to adjust a ship component, and so most of the decisions MgT made about them could be approximated in T5 if need be.
Finally, there were decisions that simply didn't matter much at all: whether landing gear overlaps in categories, and whether it takes up 1 ton versus 2 tons. Those decisions tend to balance one another out, or come out in the wash -- it only matters to truly devoted ship designers focused on one game system, and they are not likely to import a ship from another design system anyway. The problem largely solves itself.
T5 Ship Design is "Book 2 Plus"
T5 ship design has a lineage paired with flexible options. Its lineage is "classic Book 2" Traveller ship design. That becomes evident when one designs some of the fundamental, iconic traders that Traveller has always had: the decision points shrink to essentially Book 2 levels of detail:
If you focus on those essentials, ship creation is nearly Book-2-fast. And we tinkered with the T5 ship design rules early so that the results are roughly the same as those from classic Traveller.
The complexity comes in when you pay attention to the options. Ship bits can be modified by technological staging, component quality, and in some cases, range adjustments. These can be interesting and useful variables, but I treat them as outliers, and tend to ignore them.
As mentioned, MgT2 decided to change the power model for starships. Matt wanted a potential path to say "all power to shields!" and such sci fi tropes. This discontinuity only matters if you need to use those rules.
What would be helpful is a handy-dandy mapping guide between typical MgT2 power plant setups and their more typical Traveller counterparts. I'm sure such a mapping would be a fairly straightforward function, and might just require using the Mongoose formula itself on the target ship, et voila.