5400rpm HDD speeds in a USB 3.0 connectivity enclosure

Will I get better speeds from my 5400rpm hard drive when it is inside an enclosure providing USB 3.0 connectivity?

That depends what you are comparing it with. Speeds over USB (1 or 2 or 3) will be slower than directly in the laptop since you are adding protocol overhead.

Or what will the possible speeds be?

Assuming that the drive is fast enough (and most 5400 RPM laptop drives seem to yield read speeds of about 90MB/sec and slightly lower write speeds) then you will get:

• Internal: 90MB/sec
• External eSATA: 90MB/sec
• External USB2: about 30-35MB/sec (limited by USB 2 speed)
• External USB3.0 / USB3.1 gen 1 (5.0Gbit/sec): About 10x the speed from USB2. Which probably comes close to the speed of the disk when used internally with a direct SATA connection minus overhead.
• External USB3.1 gen 2 (10.0Gbit/sec): Doubles the bandwidth of USB3.0 / USB3.1 gen 1. Since your disk is probably the slowest part this does not increase performance
• External USB3 with UASP support: Significantly less overhead, but probably still limited to the same speed due as the previous one because the disk cannot saturate the channel.

That was a lot of text, now to a practical answer :)

A laptop drive is usually significantly slower than USB3's transfer speed. So you get almost the same speed when you use a slow laptop disk in an USB case as when you use it internally.

If you still need to buy an external case: Look for one which supports UAS[P].