As has been mentioned, if you've changed gauge or type of string, your intonation may be off. But I would first check for obvious setup or installation issues with the strings. Changing gauges or types of string can and will cause your intonation to be off (which can be corrected on most electric guitars by adjusting the bridge saddles) but being nearly a semitone off at the 5th fret is way, way outside the type of error you'd expect to see for an intonation issue - even after changing string type or gauge. It might be more typical to be off by half that amount, at the 12th fret. So, I would start by checking the following:
- Make sure the nut hasn't shifted. On a telecaster, the nut sits in a slot and usually stays put. But make sure it's not slipped out of position (or backwards, or otherwise incorrectly installed)
- Make sure the strings are seated well in the nut slots and break smoothly over the nut. Make sure they're routed correctly to the tuners.
- Make sure the strings are breaking correctly over the slots in the bridge saddles (versus being hung up next to the saddles or otherwise incorrectly installed).
- Make sure the bridge saddles haven't shifted. On some bridges the saddles are essentially held in place by a spring, if the saddles get tweaked during string install, the spring can get compressed and string tension can "clamp" the saddle in an incorrect position.
Finally, make sure you are deliberately setting the witness points if you're not already doing that - basically, the witness point is the point at which the string bends over the nut or the bridge saddle. In some cases, a string needs to be "set" over the witness point when first installed (by gently pressing down to crease the string). Otherwise, the string can exhibit a sort of spring-like behavior where the pitch changes as notes are fretted, which basically makes it impossible to set or maintain intonation. Often, when a string exhibits intonation issues near the extreme ends of the fretboard, it's because this is happening. It's more commonly a problem on bass guitars or other instruments with heavy strings, but it can be an issue on guitars as well, especially if the nut slots aren't well formed or the break angle over the nut or bridge are really shallow.